Sample Midterm 1 Statistics for Business
Professor Avi Giloni
1. (25 points) A Motel has 40 rooms. From past experience, the manager knows that on the average, 20%
of the people who make room reservations don’t show up. For tonight, the manager has accepted 40
reservations. If a customer with a reservation shows up, the customer pays $500 for the room.
a) What is the probability that 32 customers show up tonight? (6 points)
b) What is the probability that the motel’s revenue is $15,000 tonight? (7 points)
c) What is the expected value and standard deviation of the motel’s revenue for tonight? (12 points)
2. (15 points) On sunny days, Joe is late to work with probability .2. On non-sunny days, he is late with
probability .35. With probability .9, it will be sunny tomorrow.
a. Find the probability that Joe is not late to work tomorrow. (6 points)
b. Given that Joe is not late to work tomorrow, what is the probability that it is not sunny
tomorrow. (9 points)
3. (20 points) E(X) = 10, E(Y) = 25, Var(X) = 36, Var(Y) = 81, and Cov(3X,-2Y) = -259.2. Find
a. the correlation between X and Y,
b. E(X
2
)
c. E(Y
2
)
d. E(4XY)
e. Var(-5X+3Y)
4. One of your colleagues is interested in detecting outliers in his dataset. He decides to use a boxplot
instead of the empirical rule. He looks at his boxplot and sees that the Inter Quartile Range is equal to
0. Is this possible or was there a computer glitch? Please explain. (10 points)
5. (11 points) The number of users of an ATM machine has a Poisson Distribution with a mean of 5 per
10 minute interval.
a. Find the probability of 26 to 28 users within a 15 minute interval. (6 points)
b. Find the standard deviation of the number of users in 20 minutes. (5 points)
6. (19 points) A multiple-choice quiz has 20 questions. Each question has four possible answers, of which
only one is correct.
a. What is the probability that just guesswork will yield at least 3 correct answers? (8 points)
b. What is the expected number of correct answers by just guesswork? (4 points)
c. Suppose 5 points are awarded for a correctly answered question. What is the mean and standard
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