The Boffo Product Company sells a waffle iron on which they have done product testing. They have determined that the amount of time the prod

Question

The Boffo Product Company sells a waffle iron on which they have done product testing. They have determined that the amount of time the product will last can be described by a normal distribution. In particular, the average waffle iron lasts for 12 years and one standard deviation is 8 months. How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time

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Xavia 5 months 2021-08-27T04:38:07+00:00 1 Answers 12 views 0

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    2021-08-27T04:39:26+00:00

    Answer:

    They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.

    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.

    The average waffle iron lasts for 12 years and one standard deviation is 8 months.

    Measuring the time in months, we have that \mu = 12*8 = 96 and \sigma = 8

    How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time?

    This is X when Z has a p-value of 0.067, so X when Z = -1.5. Then

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

    -1.5 = \frac{X - 96}{8}

    X - 96 = -1.5*8

    X = 84

    84 months = 7 years.

    They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.

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