Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months, and the failure times are normally d

Question

Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months, and the failure times are normally distributed. What should be the warranty period, in months, so that the manufacturer will not have more than 7% of the blenders returned

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Thành Đạt 4 years 2021-08-08T11:38:24+00:00 1 Answers 21 views 0

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  1. ngocdiep
    0
    2021-08-08T11:39:31+00:00
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    Answer:

    The warranty period should be of 30 months.

    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 z-score 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 p-value, we get the probability that the value of the measure is greater than X.

    Optimal-Eats blender has a mean time before failure of 37 months with a standard deviation of 5 months.

    This means that \mu = 37, \sigma = 5

    What should be the warranty period, in months, so that the manufacturer will not have more than 7% of the blenders returned?

    The warranty period should be the 7th percentile, which is X when Z has a p-value if 0.07, so X when Z = -1.475.

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

    -1.475 = \frac{X - 37}{5}

    X - 37 = -1.475*5

    X = 29.6

    Rounding to the nearest whole number, 30.

    The warranty period should be of 30 months.

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