Problem 2.2

Assume that Acme Tires sells their high performance tires for $180 each and their all weather tires for $135 each. Further assume that the cost of producing a high performance tire is $150 and the cost of producing an all weather tire is $120. Finally, assume that if a tire does not last 40,000 miles, Acme tires will replace it free of charge to the consumer; Acme will incur the cost of replacement, but will not receive any additional revenue.

(a) Calculate the profit earned/loss incurred on; a high performance tire that exceeds 40,000 miles, a high performance tire that does not exceed 40,000 miles, an all weather tire that exceeds 40,000 miles, and an all weather tire that fails to last 40,000 miles.

(b) What is the expected value (expected profit) of producing an all weather tire? Of producing a high performance tire?

(c) What is the variance and standard deviation of producing an all weather tire? Of producing a high performance tire?

Problem 2.5

Assume that Acme tire life is normally distributed and that both all weather tires and high performance tires have a mean life of 50,000 miles.

1. 
   Using the probabilities you calculated in problem 2.1, calculate the standard deviations of tire life for both tire types.
2. If Acme wanted to ensure that 95% of their tires exceeded the 40,000 mile threshold, what would they have to set their warrantee at for All Weather tires? For high performance tires?

Problem 2.6

In problem 2.5, it was stated that mean tire life is 50,000 miles, and you calculated the standard deviations of tire life for each tire type. Use this information to calculate:
(a) The probability that a sample of 25 all weather tires will have an average tire life of more than 52,000 miles.
(b) The probability that a sample of 100 all weather tires will have an average life of more than 52,000 miles.
(c) The probability that a sample of 5 high performance tires will have an average life of less than 40,000 miles.
(d) The probability that a sample of 30 high performance tires will have an average life of less than 40,000 miles.

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Solution: The downloadable solution consists of 7 pages, 555 words and 1 charts.
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