# Stat 200 midterm exam spring 2020 solutions

(For Questions 1, 2, 3 and 4) There are 25 students enrolled in Stat 200 course. Their scores on Test one is written in following table 1.

10

52

69

74

64

83

74

78

77

78

58

88

64

73

71

98

75

78

90

83

72

91

81

85

64

1. (4 points) construct a frequency distribution on scores.

2. (4 points) Construct a relative frequency distribution test one scores repeated below:

scores

Frequency

50-59

2

60-69

4

70-79

10

80-89

5

90-99

3

3. (4 points) construct a histogram of the scores for the given frequency.

4. (4 points) Construct stem and leaf display for the scores in Table 1.

5. (4 points) A soda company wants to stimulate sales in this economic climate by giving customers a chance to win a small prize for every bottle of soda they buy. There is a 20% chance that a customer will find a picture of a dancing banana () at the bottom of the cap upon opening up a bottle of soda. The customer can then redeem that bottle cap with this picture for a small prize. Now, if I buy a 6-pack of soda, what is the probability that I will win something, i.e., at least win a single small prize?

6. (5 points) My brother wants to estimate the proportion of Canadians who own their house. What sample size should be obtained if he wants the estimate to be within 0.02 with 90% confidence if

a. he uses an estimate of 0.675 from the Canadian Census Bureau?

b. he does not use any prior estimates? But in solving this problem, you are actually using a form of “prior” estimate in the formula used. In this case, what is your “actual” prior estimate? Please explain.

7. (2 points) At men’s clothing store, 12 males bought green sweaters, 8 purchased blue golf sweaters, 4 bought white sweaters and 7 decided to by gray sweaters. If a customer is selected at random, calculate the probability that he bought:

(2 points)(a) Green sweater (b) blue sweater or white (c) blue or gray or white (d) A sweater which was not gray.

8. (2 points) (a) Given definition of Normal ( Gaussian distribution) by citing an example. Draw graph of the distribution.

(3 points) (b) Consider a normal distribution with a mean of 14 and variance of 26. What is the Z score for the value of 16?

Hint: Read from the text-book regarding Normal distribution and go over the power point lecture examples. Then work – out this exercise.

**Important: Please read carefully……. You are allowed to use technology for the following Problems (Problem #9 and Problem #10). Most probably, you have to use technology or you may have to spend hours, to carry out the necessary calculations by hand. Nonetheless, you should clearly delineate and explain your logic and reasoning on how to tackle problems #9, and #10.**

9. (8 points) The Undesirable Air Lines (UAL???) is notorious for its cost-cutting substandard customer service. Consequently, only 85% of the ticket holders will show up for a flight. The Air Lines workhorse, the Boring 878, has 234 seats. UAL, of course, will make extra money by overbooking. However, they have to worry about the FAA fines, and they have to keep a safety margin, say, that there is at least 95% probability that they can accommodate all those who show up for the Boring 878 flight. How many seats can they actually sell in this case?

10. (8 points) It is an open secret that airlines overbook flights, but I have just learned recently that bookstores **underbook** (I might have invented this new term.) textbooks……….

To make a long story short, our school designated virtual bookstore, MBS Direct, routinely, as a matter of business practice, orders less textbooks than the amount requested by our school’s Registrar’s Office. That is what I have figured out……. Simply put, MBS Direct has to “eat” the books if they are not sold. Do you want to eat the books? You may want to cook the books before you eat them! Oops, I hope there is no account major in this class?

OK, let us cut to the chase….. MBS Direct believes that only 85% of our registered students will stay registered in a class long enough to purchase the required textbook. Let’s pick on our STAT 200 students. According to the Registrar’s Office, we have 600 students enrolled in STAT 200 this fall 2019.

Suppose you are the CEO of MBS Direct, and you want to perform a probability analysis. What would be the number of STAT 200 textbook bundles you would order so that you stay below 5% probability of having to back-order from Pearson Custom Publishing? (*Note: Our Provost would be very angry when she hears that textbook bundles have to be back-ordered.* In any case, by next fall, we will no longer need the service of MBS Direct as we are moving 100% to free eResources. *Auf Wiedersehen*, MBS Direct……)