Assume that the average life of a refrigerator is 14 years, with the standard deviation given in part (a) before it breaks. Suppose that a c

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Assume that the average life of a refrigerator is 14 years, with the standard deviation given in part (a) before it breaks. Suppose that a company guarantees refrigerators and will replace a refrigerator that breaks while under guarantee with a new one. However, the company does not want to replace more than 6% of the refrigerators under guarantee. For how long should the guarantee be made (rounded to the nearest tenth of a year)

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Nem 3 years 2021-09-04T14:03:53+00:00 1 Answers 2 views 0

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  1. Tryphena
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    2021-09-04T14:05:50+00:00
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    Answer:

    The guarantee should be made of X = 1.555 + 14\sigma years, in which \sigma is the standard deviation given in part (a).

    Step-by-step explanation:

    Normal Probability Distribution:

    Problems of normal distributions can be solved using the z-score formula.

    In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

    Z = \frac{X - \mu}{\sigma}

    The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

    Assume that the average life of a refrigerator is 14 years

    This means that \mu = 14

    The standard deviation given in part (a) before it breaks.

    This will be the value of \sigma

    However, the company does not want to replace more than 6% of the refrigerators under guarantee. For how long should the guarantee be made?

    We need to find the 100 – 6 = 94th percentile, which is X when Z has a pvalue of 0.94. So X when Z = 1.555. So

    Z = \frac{X - \mu}{\sigma}

    1.555 = \frac{X - 14}{\sigma}

    X = 1.555 + 14\sigma

    The guarantee should be made of X = 1.555 + 14\sigma years, in which \sigma is the standard deviation given in part (a).

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