Question

Suppose you work at a large tire distribution center. The tires’ average tread life has been 50,000 miles with a standard deviation of 5,000 miles. At the end of the year, the company can reevaluate their supply contract. There are four supply options for the next contract: the current supplier or one of three competitors.

The current supplier produces tires with an average tread life of 50,000 miles with a standard deviation of 5,000 miles. Competitor A claims to produce tires with an average tread life of 52,000 miles with a population standard deviation of 8,000 miles. Competitor B claims to produce tires with an average tread life of 50,000 miles with a population standard deviation of 3,000 miles. Competitor C claims to produce tires with an average tread life of 60,000 miles with a population standard deviation of 12,000 miles.

Based on your evaluations of the three competitors, you must recommend a supply option for the next contract. Recall, you are allowed to choose the current supplier.

Answer 1

Solution:

Given

The tires’ average tread life has been 50,000 miles with a standard deviation of 5,000 miles

= 50,000

= 5,000

There are four supply options for the next contract

current supplier

average tread life of 50,000 miles with a standard deviation of 5,000 miles.

Competitor A

average tread life of 52,000 miles with a population standard deviation of 8,000 miles

Competitor B

claims to produce tires with an average tread life of 50,000 miles with a population standard deviation of 3,000 miles

Competitor C

claims to produce tires with an average tread life of 60,000 miles with a population standard deviation of 12,000 miles.

Using these samples evaluation of  the claims of the competitors is as below:

calculation:

Current Supplier:

Z = (X - )/

= (50,000 - 50,000)/5,000 = 0

Competitor A:

Z = (X - )/

= (52,000 - 50,000)/8,000 = 0.25

Competitor B:

Z = (X - )/

= (50,000 - 50,000)/3,000 = 0

Competitor C:

Z = (X - )/

= (60,000 - 50,000)/12,000 = 0.8333

Since Competitor C has the greatest Z score = 0.8333,

Competitor 3 qualifies for the next contract.

Thus, the choices for next contract are as follows:

First choice: Competitor C

Second choice: Competitor A

Third Choice: Competitor B & Current Supplier