Problem 16-03
Grear Tire Company has produced a new tire with an estimated mean lifetime mileage of 36,500 miles.
Management also believes that the standard deviation is 5000 miles and that tire mileage is normally
distributed. To promote the new tire, Grear has offered to refund some money if the tire fails to reach
30,000 miles before the tire needs to be replaced. Specifically, for tires with a lifetime below 30,000
miles, Grear will refund a customer $1 per 100 miles short of 30,000.
a.
For each tire sold, what is the expected cost of the promotion? If required, round your answer
to two decimal places.

b.
What is the probability that Grear will refund more than $50 for a tire? If required, round your
answer to three decimal places.

c.
What mileage should Grear set the promotion claim if it wants the expected cost to be $2.00?
If required, round your answer to the hundreds place.

Problem 16-09
The Iowa Energy are scheduled to play against the Maine Red Claws in an upcoming game in the
National Basketball Association Developmental League (NBA-DL). Because a player in the NBA-DL is
still developing their skills, the number of points he scores in a game can vary. Assume that each
player's point production can be represented as an integer uniform variable with the ranges provided
in the table below.
Player
Iowa Energy
Maine Red
Claws
1
[5, 20]
[7, 12]
2
[7, 20]
[15, 20]
3
[5, 10]
[10, 20]
4
[10, 40]
[15, 30]
5
[6, 20]
[5, 10]
6
[3, 10]
[1, 20]
7
[2, 5]
[1, 4]
8
[2, 4]
[2, 4]
a.
Develop a spreadsheet model that simulates the points scored by each team. What is the
average and standard deviation of points scored by the Iowa Energy? If required, round your answer to
one decimal place.

What is the shape of the distribution of points scored by the Iowa Energy?

b.
What is the average and standard deviation of points scored by the Maine Red Claws? If
required, round your answer to one decimal place.

What is the shape of the distribution of points scored by the Maine Red Claws?

c.
Let Point Differential = Iowa Energy points - Maine Red Claw points. What is the average point
differential between the Iowa Energy and Maine Red Claws? If required, round your answer to one
decimal place.

What is the standard deviation in the point differential?

What is the shape of the point differential distribution?