4s 5 Help Problem 4S-23 normally distributed with a mean of 31 years and a stand

Question

4s 5 Help Problem 4S-23 normally distributed with a mean of 31 years and a standard deviation of Auto batteries have an average life of 31 years. Battery life is 0.46 year. The batteries 10 are warranted to operate for a minimum of 2 years. If a battery fails within the warranty period, it will be replaced with a new battery at no charge. The compeny sells and installs the batteries. Also, the usual $4 installation charge will be waived. a. What percentage of batteries would you expect to fail before the warranty period expires? (Round your z value to 2 decimal places. Round probabilities to 4 decimal places. Round your final answer to 2 decimal places. Omit the"%" sign in your response.) Percentage-% b. A competitor is offering a warran ty of 30 months on its premium battery. The manager of this company is toying with the idea of offering a 30-month warranty on it. What centage of the batteries would you expect to fail before this new warranty period expires? (Round your z value to 2 places. Round probabilities to 4 decimal places. Round your final answer to 2 decimal places. Omit t he "%" sign in your response.) Percentage

Explanation / Answer

(a) Corresponding z value is given by

z = x - mu / sigma where mu = 3.1

x = 2 and sigma = 0.46

z = 2-3.1 / 0.46 = -2.39

which corresponds to 0.00842 which means 0.842% of batteries will fail before 2 yrs.

(b) For 30 months warrenty case, we need to replace 2 yrs, in the part (a) with 2.5 years

now z = 2.5-3.1 /0.46 = -1.303

which corresponds to 0.0968.

In this case 9.68% batteries will fail before warranty period.

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