The average life of a certain type of small motor was estimated to be 10 years with a standard deviation of 2 years. The manufacturer of the motor wants to issue a policy that will replace all motors that fail while under guarantee free of cost. If the company has budget to replace only 3% of all the motors that fail, how long a guarantee (in years) should they offer? You may assume that the lives of the motors are normally distributed.

Question

Trey Butler

Computers & Technology

11 November, 19:14

The average life of a certain type of small motor was estimated to be 10 years with a standard deviation of 2 years. The manufacturer of the motor wants to issue a policy that will replace all motors that fail while under guarantee free of cost. If the company has budget to replace only 3% of all the motors that fail, how long a guarantee (in years) should they offer? You may assume that the lives of the motors are normally distributed.

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Answers (1)

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Roger · Answer 1

The answer is 6.24 years

Explanation:

Given that,

let estimated year is "a" = 10 year

let standard deviation of year is " b" = 2 year

so,

using the normal standard table

P (z
P (z
P (z< - 1.881) = 0.03

than, z = - 1.881

using z-score formula

X = zb + a

X = - 1.881 * 2 + 10

X = 6.24 year