A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 17 years with

Question

A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 17 years with a standard deviation of 4 years. If the claim is true, in a sample of 48 wall clocks, what is the probability that the mean clock life would be greater than 18 years

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Autumn 2 months 2021-10-08T22:47:50+00:00 1 Answer 0 views 0

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    2021-10-08T22:49:31+00:00

    Answer:

    Probability that the mean clock life would be greater than 18 years is 0.04182 .

    Step-by-step explanation:

    We are given that the designer claims they have a mean life of 17 years with a standard deviation of 4 years.

    Let X bar = mean clock life

    The z score probability distribution is given by;

                 Z = \frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

    where,  \mu = population mean life = 17 years

                \sigma = standard deviation = 4 years

                n = sample of wall clocks = 48

    So, the probability that the mean clock life would be greater than 18 years is given by, P(X bar > 18 years);

       P(X bar > 18) = P( \frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{18 - 17}{\frac{4}{\sqrt{48} } } ) = P(Z > 1.73) = 1 – P(Z <= 1.73)

                                                                                  = 1 – 0.95818 = 0.04182

    Therefore, the probability that the mean clock life would be greater than 18 years is 0.04182 .

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