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Probability and Expectation Problems

1. The high school GPA of applicants for admission to a college program are recorded and relative frequencies are calculated for the categories.

GPA f(x)

x < 2.0 .08
2.0 <= x < 2.5 .12
2.5 <= x < 3.0 .35
3.0 <= x < 3.5 .30
3.5 <= x ?

a. Complete the table to make this a valid probability distribution.
b. What is the probability an applicant's GPA will be below 3.0?
c. What is the probability an applicant's GPA will be 2.5 or above?

2. A video rental store has two video cameras available for customers to rent. Historically, demand for cameras has followed this distribution. The revenue per rental is $40. If a customer wants a camera and none is available, the store gives a $15 coupon for tape rental.

Demand Relative Frequency Revenue Cost
0 .35 0 0
1 .30 40 0
2 .20 80 0
3 .10 80 15
4 .05 80 30

a. What is the expected demand?
b. What is the expected revenue?
c. What is the expected cost?
d. What is the expected profit?

3. A manufacturer of computer disks has a historical defective rate of .001. What is the probability that in a batch of 1000 disks, 2 would be defective?

(note: answer using either the relevant probability table in the back of the book, or use the relevant probability function on your calculator / Excel).

4. After a severe winter, potholes develop in a state highway at the rate of 5.2 per mile. Thirty-five miles of this highway pass through Washington County.
a. How many potholes would you expect to see in the county?
b. What is the probability of finding 8 potholes in 1 mile of highway?

5. Customers at a popular restaurant that refuses reservations arrive according to the Poisson distribution at a rate of 4 parties every 5 minutes. What is the probability that there will be more than 2 minutes between arriving parties?

Solution Summary

The solution gives complete details of computing probability and expectation for binomial and Poisson random variables.