Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and

Question

Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years. You want to set the warranty on your product so that you do not have to replace more than 5% of the hot water heaters that you sell. How many years should you claim on your warranty

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Ximena 2 months 2021-10-09T22:22:45+00:00 1 Answer 0 views 0

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    2021-10-09T22:24:30+00:00

    Answer:

    You should claim 10.5325 years on your warranty.

    Step-by-step explanation:

    Problems of normally distributed samples are 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.

    In this problem, we have that:

    \mu = 13, \sigma = 1.5

    Want’s to replace no more than 5% of the products.

    This means that the warranty should be 5th percentile, that is, the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.

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

    -1.645 = \frac{X - 13}{1.5}

    X - 13 = -1.645*1.5

    X = 10.5325

    You should claim 10.5325 years on your warranty.

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