Basic Statistics

Basic Statistics.  

1. The following frequency histogram shows the scores for seventeen students in a quiz.

 

 

1. (2 pts) Find the number of students who scored less than 60 on the quiz.

 

 

1. (2 pts) Find the percentage of students who scored 80 or higher.

 

 

 

 

1. (5 pts) Find the approximate mean.

 

 

 

 

 

 

2. Given the following set of data of nine night temperatures

-2, 0, 0, 4, -2, 1, 6, -1, 0

3. (6 pts) Find Q1, Q2 and Q3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (1 pts) Find the interquartile range (IQR)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) Draw a box-plot and comment on the shape of the distribution.

 

 

 

 

 

 

 

 

 

 

 

3. Consider the following two variables X and Y:

X	1	1	4	15
Y	8	9	5	0

1. (2 pts) Find the mean of X, and mean of Y

 

 

 

 

1. (2 pts) Find the standard deviation of X, and standard deviation of Y

 

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the covariance between X and Y.

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find correlation between X and Y and comment on your answer.

 

 

 

 

4. Male and Female students at a high school were surveyed about their career preferences. The data are shown in the table below.

 

	Doctor	Engineer	Other
Male	10	12	25
Female	15	8	27

 

 

1. (2 pts) What is the probability that a randomly selected student wants to be an Engineer?

 

 

 

1. (2 pts) What is the probability that a randomly selected student is a Female and wants to be a Doctor?

 

 

 

 

1. (3 pts) What is the probability that a randomly selected student wants to be a Doctor, given that the student is Male?

 

 

 

 

 

1. (3 pts) What is the probability that a randomly selected student is Male, given that this student wants to be Doctor?

 

 

5. The random variable Y can take values -1, 0, 1 and 2 only. The probability distribution of Y is given below.

Y	P(Y)
-1	0.05
0	0.30
1	0.20
2	c

1. (2 pts) Find the value of c.

 

 

 

 

1. (2 pts) What is the probability that Y is less than or equal to 1? (i.e. ) )

 

 

 

1. (2 pts) Find the expected value of Y.

 

 

 

 

 

 

 

 

6. 1. (3 pts) A team is being formed that includes 11 different people. There are different positions on the team. How many different ways are there to assign the 11 people to the 11 positions?

 

 

 

 

 

1. (3 pts) A student has 9 course books that she would like to place in her However, she only has room for 3 books. Regardless of the arrangement, how many ways are there she can select 3 books into her backpack?

 

 

 

7. In a hospital, 40% of the patients are male. 12% of the male patients have disease X, and 20% of the female patients do not have disease X.
   1. (2 pts) If a patient is selected at random, what is the probability that the patient has disease X?

 

 

 

 

 

 

1. (2 pts) If a patient is selected at random, what is the probability that the patient is a female and have disease X?

 

 

 

 

 

1. (2 pts) Given that a randomly selected patient does not have disease X, what is the probability that the patient is male?

 

8. Suppose that you and two friends go to a restaurant, which last month completed approximately 85% of orders correctly. Assume a binomial distribution.
   1. (3 pts) What is the probability that all 3 orders will be completed correctly?

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that at least one order is completed correctly?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) What is the expected number of correctly completed orders?

 

 

 

 

 

 

 

 

 

 

 

 

9. Assume that the number of network errors experienced in a day on a Local Area Network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced is 1.7 per day.
10. (3 pts) What is the probability that on a given day there are no errors?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that on a given day there are 1 or 2 errors?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that there are exactly 5 errors in 2 days?

 

 

 

 

 

 

 

 

 

 

 

10. The annual ground coffee expenditures for households are approximately normally distributed, with a mean of $49 and a standard deviation of $13.

 

25. (3 pts) Find the probability that a household spent less than $25.

 

 

 

 

 

 

 

 

 

 

 

50. (3 pts) Find the probability that a household spent more than $50.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) What proportion of the households spent between $22 and $30?

 

 

 

 

 

 

 

 

 

98. (2 pts) 98.5​% of the households spent less than what​ amount?

 

 

 

 

 

11. A study of the time spent shopping in a supermarket for specific items showed an approximately uniform distribution between 20 minutes and 45
12. (2 pts) Write the probability density function and graph it.

 

 

 

 

 

 

 

 

 

1. (2 pts) What is the probability that the shopping time will be between 32 and 38 minutes?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) What are the mean and standard deviation of the shopping time?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

12. The weights of newborn babies are normally distributed with a mean of 3.05 kg and a standard deviation of 0.45 kg. A random sample of 25 newborn babies is selected.

 

1. (2 pts) What is the standard error for the sample mean?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2. (6 pts) What is the probability that the sample mean weight of babies is less than 2.80 kg?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cover page

 

 

13. The following frequency histogram shows the number of goal scores in first twenty days of a football

 

1. (2 pts) Find the number of goals scored in first 15 days of the tournament.

 

 

1. (2 pts) Find the percentage of the goal scored in first 5 days.

 

 

 

1. (5 pts) Make a cumulative percentage polygon (OGIVE).

 

 

 

 

 

 

 

14. Given the following set of data of seven days in winter temperatures

0, 4, 2, 1, 5, 1, 0

3. (3 pts) Find Q1, Q2 and Q3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find the mode.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) Draw a box-plot and comment on the shape of the distribution.

 

 

 

 

 

 

 

 

 

 

 

15. Consider the following two variables X and Y:

X	2	3	4	7
Y	6	8	6	0

1. (2 pts) Find the mean of X, and mean of Y.

 

 

 

 

1. (2 pts) Find the standard deviation of X, and standard deviation of Y.

 

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the covariance between X and Y.

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find correlation between X and Y and comment on your answer.

 

 

 

 

16. Male and female students at a high-school were surveyed about their food preferences. The data are shown in the table below.

 

	Fish	Chicken	Lamb	Total
Male	40	130	80
Female	100	70	260
Total

 

1. (2 pts) If you randomly select a student, what is the probability that the student prefers chicken?

 

 

 

1. (2 pts) What percent of the students do not prefer fish?

 

 

 

 

1. (3 pts) If you randomly select a student, what is the probability that the student is male and not prefers fish?

 

 

 

 

 

1. (3 pts) What is the probability that a randomly selected student is male, given that he prefers fish?

 

 

17. The random variable Y can take values -1, 0, 1 and 2 only. The probability distribution of Y is given below.

Y	P(Y)
-1	0.1
0	0.3
1	0.2
2	0.4

 

1. (2 pts) What is the probability that Y is less than or equal to 0 (i.e. ) ) ?

 

 

 

1. (3 pts) Find the expected value of Y.

 

 

 

 

 

 

 

 

18. 1. (3 pts) 25 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?

 

 

 

 

 

 

 

 

 

 

1. (5 pts) A bag contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the bag, if at least one black ball is to be included in the draw?

 

 

 

 

19. In a company, 60% of the employees are male. 20% of the male employees are married, and 40% of the female employees are not married.
    1. (2 pts) If an employee is selected at random, what is the probability that the employee is married?

 

 

 

 

 

 

1. (2 pts) If an employee is selected at random, what is the probability that the employee is a female or married?

 

 

 

 

 

1. (2 pts) Given that a randomly selected employee is not married, what is the probability that the employee is female?

 

20. In medical doctors MRCP exam in UK, 10% of the doctors pass the test. Assuming a Binomial probability distribution model, what is the probability that among the next 10 applicants.
    1. (3 pts) Exactly 8 will pass?

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) More than 3 will fail?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) At least 1 will pass?

 

 

 

 

 

 

 

 

 

 

 

 

21. Motorists arrive in a McDonald’s restaurant at a rate of 2 per minute. We are assuming a Poisson probability distribution model.
22. (3 pts) What is the probability that more than three motorists will arrive in McDonald’s during a 1 minute interval?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that exactly six motorists will arrive in McDonald’s during a

5 minute interval?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) How many motorists can an employee expect in his 4 hour shift?

 

 

 

 

 

 

 

 

 

 

 

22. The average high-school teacher annual salary is $43,000. Let the teacher salary be normally distributed with a standard deviation of $18,000.

 

1. (3 pts) What percent of high-school teachers make more than $70,000?

 

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) What percent of high-school teachers make between $40,000 and $50,000?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) 30​% of the teacher salary more than what ​amount?

 

 

 

 

 

23. The length of time it takes to complete a background security check is uniformly distributed and varies between 60 and 70 minutes.
24. (2 pts) Compute the probability that security check will take between 55 and 75 minutes?

 

 

 

 

 

 

 

 

1. (2 pts) Compute the probability that a security check will take less than 70 minutes to complete?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) What are the mean and standard deviation of the security check?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

24. According to a recent study, university students average 100 text messages daily. Assume the population standard deviation is 20 text messages. Suppose a random sample of 49 students is taken.

 

1. (2 pts) What is the standard error for the sample mean?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (6 pts) What is the probability that the sample mean is between 95 and 105 messages?

 

 

 

 

 

 

 

 

 

 

 

 

 

Cover page

 

 

1. (3pts) Complete the following frequency distribution

 

Classes	Frequency	Relative Frequency	Percentage  (%)	Cumulative Percentage
0 but less than 4	6
4 but less than 8	8
8 but less than 12
12 but less than 16	5
16 but less than 20	2
Total	25

2. (3 pts) Plot a histogram of frequencies.

 

 

 

 

 

 

3. (3pts) Plot a cumulative percentages polygon (OGIVE)

 

 

 

 

 

 

 

 

 

 

 

 

1. Given the following set of data

13, 6, 8, 13, 15, 18, 11, 16, 17, 15

1. (3 pts) Find the range, the median, and the mode.

 

 

 

 

 

 

 

 

 

 

3. (2 pts) Find Q1 and Q3.

 

 

 

 

 

 

 

 

 

 

1. (3 pts) Draw box-plot and comment on the shape of the distribution.

 

 

 

 

 

 

 

 

 

 

1. (4 pts) If the mean of given data is 25 and the standard deviation of the data is 3, conclude whether 36 is an outlier or not?

 

 

 

 

 

 

1. Consider the following two variables X and Y:

X	3	7	9	13
Y	4	6	16	2

1. (3 pts) Make a scatter plot

 

 

 

 

 

 

 

1. (2 pts) Find the mean of X and the mean of Y.

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the correlation between X and Y and comment on your result.

 

 

 

 

 

 

 

 

1. Consider the following table about the Brand and Color of 200 cars

 

	Toyota	Honda	Nissan
White	32	20	28
Not White	38	46	36

 

1. (3 pts) What is the probability that a randomly selected car is White?

 

 

 

1. (3 pts) What is the probability that a randomly selected car is White and not Toyota?

 

 

 

 

• (3 pts) What is the probability that a randomly selected car is White or Honda?

 

 

 

 

1. (3 pts) If you randomly select a White car, what is the probability that it is Nissan?

 

 

 

                 

1. (6 pts) Consider the following probability distribution:

X	P(X)
2	0.35
3	c
4	0.1
5	0.4

1. Find the value of c.

 

 

1. What is the probability that X is greater than 3

 

 

 

• Find the expected value of X.

 

 

 

 

 

 

 

 

 

1. (6 pts) Suppose that during the Fall 2015 semester, there are 5 elective courses and 3 major courses available for registration.

1. In how many different ways can you select 3 elective courses and 2 major courses?

 

 

 

 

 

 

1. In how many different ways can you select 3 elective courses and 2 major courses, if the elective course PHYS100 has to be selected?

 

 

 

 

1. In            a              basic      Mathematics     course,                 80%        of            the         enrolled               students                 pass       the         course.

Given a section of 12 students; and assuming a binomial probability distribution model

1. (3 pts) what is the probability that exactly 9 students will pass the course?

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) what is the probability that no student will fail the course?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• (2 pts) what is the expected number of students who will pass the course?

 

 

 

 

 

 

 

 

 

 

 

 

1. In a computer network, the average of network communication errors is 2 per hour. Assuming a

Poisson’s probability distribution model

1. (3 pts) what is the probability that there will be at most one communication error in an hour?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) what is the probability that there will be more than two communication errors in an hour?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) what is the probability that there will be exactly 6 communication errors in 4 hours?

 

 

 

 

 

 

 

 

 

 

                 

1. Statistically  it is shown that the temperature in a city is normally distributed with mean 22°C and  standard deviation of 8° C. Find the probability that at a random day:

 

1. (3 pts) The temperature will be greater than 20°C?

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) The temperature will be between 14°C and 26°C?

 

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) If the probability that the temperature doesn’t exceed t is equal to 0.6, find the value of t? (e. find t such that P( X < t) = 0.6)

 

 

 

 

 

 

                 

1. The waiting time for an elevator is uniformly distributed and varies between 10 and 60 seconds

1. (2 pts) Write the probability density function.

 

 

 

 

 

1. (3 pts) What is the probability that the waiting time for this elevator is less than 30 seconds?

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that the waiting time for this elevator is between 5 and 20 seconds?

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) What is the expected waiting time for this elevator and what is the standard deviation?

 

 

 

 

 

 

 

 

 

 

 

                 

1. The weights of the contents of pasta sauce cans produced by a company are normally distributed with a mean of 7 ounces and a standard deviation of 0.5 ounces. A random sample of 16 cans is selected.

1. (3 pts) What is the standard error for the sample mean?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. (5 pts) What is the probability that the sample mean weight of pasta sauce cans is less than 6.9 ounces?

 

 

 

 

 

 

Cover page

 

 

4. Given the following frequency distribution.

 

Classes	Classes Midpoints	Frequency	Percentage  (%)	Cumulative Percentage
5 but less than 10		6
10 but less than 15		11
15 but less than 20		14
20 but less than 25		9

 

1. (3 pts) Fill in the table above.

 

2. (3 pts) Plot a frequency histogram.

 

 

 

 

 

 

3. (3 pts) Find the approximate mean of this frequency distribution.

 

 

 

 

 

 

 

 

 

 

 

 

 

5. Given the following set of data

19, 23, 27, 28, 30, 31, 32, 33, 33, 35

1. (3 pts) Find the
   1. Median

 

 

 

1. Mode

 

 

 

1. Range

 

 

 

 

 

3. (2 pts) Find Q1 and Q3.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Draw a box-plot.

 

 

 

 

 

 

 

 

6. The following table represents the price (P) and demand (D) for a given product:

Price (P)	5	10	15	20
Demand (D)	20	13	9	2

1. (4 pts) Find the mean of P and the mean of D.

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the standard deviation of P and the standard deviation of D.

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the correlation between the price and the demand, then comment on your result.

 

 

7. The following data represent some statistics about students in a College, depending on their major and their order of seniority.

 

	Finance	Management	Business	Total
Freshman	30	80	65	175
Junior	110	225	140	475
Senior	70	35	45	150
Total	210	340	250	800

 

1. (3pts) What is the probability that a randomly selected student is Junior and Business major?

 

 

 

1. (3pts) What is the probability that a randomly selected student is not Senior?

 

 

 

 

1. (3pts) What is the probability that a randomly selected student is a Freshman or Management major?

 

 

 

 

1. (3pts) What is the probability that randomly selected student is Finance major, given that he/she is Senior?

 

 

         

1. The customers of an Electronics shop were asked whether they preferred iPad or Samsung tablet. 70% of the customers are males. 45% of the males preferred Samsung tablet, while 60% of the females preferred iPad.
   1. (4 pts) Find the probability that a customer prefers iPad.

 

 

 

 

 

 

 

 

 

1. (4 pts) Given that a customer prefers Samsung Tablet, find the probability that he is a male.

 

 

 

 

 

 

 

 

 

 

 

1. (7 pts)
   1. You have 6 new books and 5 new DVD movies. How many different ways can you select 3 books to read and 2 movies to watch?

 

 

 

 

 

 

 

 

1. 7 swimmers are participating in a competition. The first three of them will receive ordered awards (Gold, Silver, and Bronze). In how many different ways can the 3 awards be distributed?

 

 

 

 

 

 

1. On a Math Placement Test, only 35% of the candidates pass the Test. If 8 candidates take this Test, assuming a binomial distribution,
   • (3 pts) find the probability that no more than one candidate will pass this Test?

 

 

 

 

 

 

 

 

 

 

 

 

 

• (3 pts) find the probability that exactly two candidates fail this Test?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• (2 pts) Find the expected number of candidates who would pass this Test?

 

 

 

 

 

 

 

 

 

 

 

2. Motorists arrive to a gas station at a rate of 2.7 per minute. Assuming a Poisson’s probability distribution model,
   1. (3 pts) find the probability that no motorist will arrive to the gas station in a given minute?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) find the probability that at least 2 motorists will arrive to the gas station in a minute?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

• (3 pts) find the probability that exactly 12 motorists will arrive to the gas station in 5 minutes?

 

 

 

 

 

 

 

 

 

 

         

1. The waiting time in a doctor’s office is uniformly distributed and varies between 5 and 25 minutes
   1. (2 pts) Calculate the expected waiting time and its standard deviation.

 

 

 

 

 

 

 

 

 

1. (2 pts) Write the probability density function.

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that a patient will wait between 10 and 15 minutes?

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that a patient will wait more than 15 minutes?

 

 

 

 

 

 

 

 

 

         

10. A radar unit is used to measure the speeds of cars on an expressway. The speeds are normally distributed with a mean of 98 and a standard deviation of 10.
    1. (3pts) Find the probability that a randomly selected car is travelling at less than 120?

 

 

 

 

 

 

 

 

 

 

 

1. (3pts) Find the probability that a randomly selected car is travelling at a speed between 80 and 105?

 

 

 

 

 

 

 

 

 

 

 

 

1. (4pts) Find the speed s that determines the 15% fastest cars (e. find s such that p (X > s) = 0.15)

 

 

 

 

 

 

 

         

1. The size of an electronic component is normally distributed with a mean of 36 millimeters and a standard deviation of 16 millimeters. A random sample of 25 components is selected.

 

1. (4 pts) What is the standard error for the sample mean?

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the probability that the sample mean size of the components will be between 35 and 40 millimeters?

 

 

 

 

 

 

Cover page

 

 

25. Given the following frequency distribution of Final exam scores for College Algebra.

 

 

 

 

1. (3 pts) Fill in the table above.
2. (3 pts) Plot a percentage histogram.

 

 

 

 

 

 

 

 

 

1. (3 pts) Find the approximate mean of this frequency distribution.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

26. Given the following set of data

26, 13, 27, 25, 26, 20, 18, 29, 23.

1. (4 pts) Find the mean, median, mode and range.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find Q1, Q2, Q3, and IQR.

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Draw box-plot.

 

 

 

 

 

27. Consider the following two variables X and Y:

 

X	11	14	7	12
Y	3	9	12	16

1. (2 pts) Find the mean of X and the mean of Y.

 

 

 

 

 

 

1. (4 pts) Find the covariance between X and Y and comment on your result.

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the standard deviation of X and the standard deviation of Y.

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find the correlation between X and Y and comment on your result.

 

 

28. The following data is observed from a survey about the preference of customers as their choice of car.

	Toyota	Kia	Nissan	Total
Male	160	31	130	425
Female	40	135	75	250
Total	270	260	140	700

 

1. (2 pts) Complete the table.
2. (2 pts) What is the probability that a randomly selected person drives Kia?

 

 

 

1. (3 pts) What is the probability that a randomly selected person is a male and drives Toyota?

 

 

 

 

1. (3 pts) What is the probability that a randomly selected person is a male or drives Nissan?

 

 

 

 

 

1. (2 pts) Given a randomly selected person drives Toyota, what is the probability that the person is male?

 

 

 

 

29. (5 pts) Students in a certain community were surveyed. Among these students 80% indicated that they have a laptop. Of those who have a laptop, 90% have a smart cell phone. Of those who do not own a laptop, 70% have a smart cell phone.

 

Find the probability that a randomly selected student owns both a smart cell phone and a laptop?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

30. (6 pts)
    1. GUST offers 12 elective courses in the Spring Semester. You have to choose 3 elective courses. How many possible schedules can be selected?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. In how many different ways can we select 2 instructors and 3 teaching assistants for a proctoring from 5 instructors and 7 teaching assistants?

 

 

 

 

31. Suppose that probability of a person having Twitter account is 0.4. We have a group of 10 people. Assuming a binomial distribution,
32. (3 pts) find the probability that exactly 3 people have Twitter account?

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) find the probability that at most 1 person has Twitter account?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) find the expected number of people having Twitter accounts and the variance of people having Twitter accounts.

 

 

 

 

 

 

 

 

 

 

 

32. Based on past data, the average number of accidents happen in airport is 4.5 per day.
    (Hint: Poisson distribution)
33. (3 pts) What is the probability that exactly 3 accidents in a day?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that at least one accident happens in a day?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that at most 2 accident happens in three days?

 

 

 

 

 

 

 

 

 

 

 

33. The production time of a Samsung tablet is normally distributed with a mean of 8 minutes and a standard deviation of 5 minutes.

 

8. (3 pts) What is the probability that the production time of a randomly selected Samsung tablet is less than 8.6 minutes?

 

 

 

 

 

 

 

 

 

 

 

8. (3 pts) What is the probability that the production time of a randomly selected Samsung tablet is greater than 8.6 minutes?

 

 

 

 

 

 

 

 

 

 

 

 

8. (4 pts) What is the probability that the production time of a randomly selected Samsung tablet is between 8 and 8.6 minutes?

 

 

 

 

 

 

 

10. 10. The waiting time in the coffee shop is uniformly distributed and varies between 30 and 80 seconds.
11. (3 pts) Write the probability density function.

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that the waiting time for the coffee is less than 50 seconds?

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that the waiting time for the coffee is between 20 and 60 seconds?

 

 

 

 

 

 

 

 

 

1. (2 pts) Calculate the expected amount of time it takes to wait in the coffee shop.

 

 

 

 

 

11. Assume that the weight of a person has a normal distribution with a mean of 80 kilograms and a variance of 64. A random sample of 36 persons is selected.

 

1. (4 pts) What is the standard error for the sample mean?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (5 pts) What is the probability that the sample mean weight of persons is between 76 and 84 kilograms?

 

 

 

 

 

 

Cover page

 

 

34. Given the following frequency distribution of Final exam scores for College Algebra.

 

 

 

 

1. (3 pts) Fill in the table above.
2. (3 pts) Plot a cumulative percentage polygon (OGIVE).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) Find the approximate mean of this frequency distribution.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

35. Given the following set of data

26, 13, 27, 25, 26, 20, 18, 29, 23.

1. (4 pts) Find the mean, median, mode and range.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find Q1, Q2, Q3, and IQR.

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Draw box-plot.

 

 

 

 

 

36. Consider the following two variables X and Y:

 

X	11	14	7	12
Y	3	9	12	16

1. (2 pts) Find the mean of X and the mean of Y.

 

 

 

 

 

 

1. (4 pts) Find the covariance between X and Y and comment on your result.

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the standard deviation of X and the standard deviation of Y.

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find the correlation between X and Y and comment on your result.

 

 

37. The following data is observed from a survey about the preference of customers as their choice of car.

	Toyota	Kia	Nissan	Total
Male	160	31	130	425
Female	40	135	75	250
Total	270	260	140	700

 

1. (2 pts) Complete the table.
2. (2 pts) What is the probability that a randomly selected person drives Kia?

 

 

 

1. (3 pts) What is the probability that a randomly selected person is a male and drives Toyota?

 

 

 

 

1. (3 pts) What is the probability that a randomly selected person is a male or drives Nissan?

 

 

 

 

 

1. (2 pts) Given a randomly selected person drives Toyota, what is the probability that the person is male?

 

 

 

 

38. (5 pts) Students in a certain community were surveyed. Among these students 80% indicated that they have a laptop. Of those who have a laptop, 90% have a smart cell phone. Of those who do not own a laptop, 70% have a smart cell phone.

 

Find the probability that a randomly selected student owns both a smart cell phone and a laptop?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

39. (6 pts)
    1. GUST offers 12 elective courses in the Spring Semester. You have to choose 3 elective courses. How many possible schedules can be selected?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. In how many different ways can we select 2 instructors and 3 teaching assistants for a proctoring from 5 instructors and 7 teaching assistants?

 

 

 

 

40. Suppose that probability of a person having Twitter account is 0.4. We have a group of 10 people. Assuming a binomial distribution,
41. (3 pts) find the probability that exactly 3 people have Twitter account?

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) find the probability that at most 1 person has Twitter account?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) find the expected number of people having Twitter accounts and the variance of people having Twitter accounts.

 

 

 

 

 

 

 

 

 

 

 

41. Based on past data, the average number of accidents happen in airport is 4.5 per day.
    (Hint: Poisson distribution)
42. (3 pts) What is the probability that exactly 3 accidents in a day?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that at least one accident happens in a day?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that at most 2 accident happens in three days?

 

 

 

 

 

 

 

 

 

 

 

42. The production time of a Samsung tablet is normally distributed with a mean of 8 minutes and a standard deviation of 5 minutes.

 

8. (3 pts) What is the probability that the production time of a randomly selected Samsung tablet is less than 8.6 minutes?

 

 

 

 

 

 

 

 

 

 

 

8. (3 pts) What is the probability that the production time of a randomly selected Samsung tablet is greater than 8.6 minutes?

 

 

 

 

 

 

 

 

 

 

 

 

8. (4 pts) What is the probability that the production time of a randomly selected Samsung tablet is between 8 and 8.6 minutes?

 

 

 

 

 

 

 

10. 10. The waiting time in the coffee shop is uniformly distributed and varies between 30 and 80 seconds.
11. (3 pts) Write the probability density function.

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that the waiting time for the coffee is less than 50 seconds?

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that the waiting time for the coffee is between 20 and 60 seconds?

 

 

 

 

 

 

 

 

 

1. (2 pts) Calculate the expected amount of time it takes to wait in the coffee shop.

 

 

 

 

 

11. Assume that the weight of a person has a normal distribution with a mean of 80 kilograms and a variance of 64. A random sample of 36 persons is selected.

 

1. (4 pts) What is the standard error for the sample mean?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (5 pts) What is the probability that the sample mean weight of persons is between 76 and 84 kilograms?

 

 

 

 

 

 

Cover page

 

 

 

43. (9 pts) Array represents the exam scores for 10 students for College Algebra.

 

25    32    36    48   50   62   67   75   88   90

 

 

1. (3 pts) Fill in the table below.

 

 

 

 

 

1. (3 pts) Plot a percentage histogram.

 

 

 

 

 

 

 

1. (3 pts) Find the approximate mean (group mean) of this frequency distribution using midpoint of classes.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

44. (8 pts) Given the following set of data

25, 10, 20, 28, 16, 10, 14, 10, 24.

1. (4 pts) Find the mean, median, mode and range.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find quartiles, Q1, Q2, Q3, and inter quartile range IQR.

 

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Draw box-plot and comment on the shape of the data

 

 

 

 

 

 

45. (12 pts) Consider the following two variables X and Y:

 

X	8	2	6	12
Y	3	13	11	17

1. (2 pts) Find the mean of X and the mean of Y.

 

 

 

 

 

 

1. (4 pts) Find the covariance between X and Y and comment on your result.

 

 

 

 

 

 

 

 

 

 

 

1. (4 pts) Find the standard deviation of X and the standard deviation of Y.

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Find the correlation between X and Y and comment on your result.

 

 

 

46. (12 pts) The following data is observed from a survey about the ownership of customers as their choice of tablet.

	Apple	Samsung	Lenovo	Total
Male	160	a31	90	330
Female	40	135	75	250
Total	250	290	140	700

 

1. (3 pts) Complete the table.
2. (3 pts) What is the probability that a randomly selected person owns Apple?

 

 

 

 

1. (3 pts) What is the probability that a randomly selected person is a female or uses Apple?

 

 

 

 

 

1. (3 pts) Given that a randomly selected person is a male, what is the probability that the person uses Apple?

 

 

 

 

47. (5 pts) Students in a certain school were surveyed. Among these students 80% are female. Of those who are male, 90% have a Facebook account. Of those female, 35% has a Facebook account.

 

1. Find the probability that a randomly selected student is male and does not own a Facebook account?

 

 

 

 

 

 

1. Find the probability that a randomly selected student is male given she does not own a Facebook account?

 

 

 

 

 

 

 

 

 

 

48. (6 pts) For the fall semester, there are 7 major courses and 8 elective courses available to register.
    1. In how many different ways can you register to 2 major courses and 3 elective courses?

 

 

 

 

 

 

 

 

 

1. If you have to register to MATH 121 as a major course and BIOL 110 as an elective course, in how many different ways can you register to 3 major courses and 2 elective courses?

 

 

 

 

49. (9 pts) Suppose that the probability of a person having an online banking account is 0.7. We have a group of 12 people. Assuming a binomial distribution,
50. (2 pts) find the probability that exactly 4 people have online banking account.

 

 

 

 

 

 

 

1. (2 pts) find the probability that at most 1 person has online banking account.

 

 

 

 

 

 

 

 

 

1. (2 pts) find the probability that 4 people does not have online banking account.

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) find the expected number of people having online banking accounts and the variance of people having online banking accounts.

 

 

 

 

 

 

 

 

 

 

 

 

50. (9 pts) Based on past data, the average number of emergency calls in Mishref is 4 per day.
    (Hint: Poisson distribution)
51. (3 pts) What is the probability of at most 1 emergency call in a day?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability of at least 1 emergency call in a day?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability of no emergency calls in two days?

 

 

 

 

 

 

 

 

 

 

 

 

51. (10 pts) X is normally distribution with a mean of 8 and a standard deviation of 5. Evaluate the following probabilities;

 

1. (2 pts) P(10 <X )

 

 

 

 

 

 

 

 

 

 

1. (3 pts) P(7 < X < 10)

 

 

 

 

 

 

 

 

1. (2 pts) P(30 < X )

 

 

 

 

 

 

 

 

1. (3 pts) Find the value of t so P(X < t)=0.7

 

 

 

 

 

 

 

 

 

10. 10. (11 pts) The waiting time in the Starbucks is uniformly distributed and varies between 50 and 80 seconds.

1. (3 pts) What is the probability that the waiting time for the coffee is less than 60 seconds?

 

 

 

 

 

 

 

 

 

 

1. (3 pts) What is the probability that the waiting time for the coffee is between 70 and 100 seconds?

 

 

 

 

 

 

 

 

 

 

 

1. (2 pts) Calculate the expected amount of time it takes to wait in the coffee shop.

 

 

 

 

 

 

11. (9 pts) According to a recent survey, high school students average 100 text messages daily which has a normal distribution. Assume the population standard deviation is 28 text messages. Suppose a random sample of 49 students is taken.

 

1. (3 pts) What is the standard error for the sample mean?

 

 

 

 

 

 

 

 

 

 

1. (6 pts) What is the probability that the sample mean is between 85 and 100 messages?

 

 

 

 

 

 

 

Basic Statistics

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