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27 November, 14:34

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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  1. 27 November, 17:29
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    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
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