The tread life of tires mounted on light duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard

Question

The tread life of tires mounted on light duty trucks follows the normal probability distribution with a mean of 60,000 miles and a standard deviation of 4,000 miles. Suppose you bought a set of four tires, what is the likelihood the mean tire life of these four tires is more than 66,000 miles?

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Melody 2 weeks 2021-09-09T09:26:23+00:00 1 Answer 0

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    2021-09-09T09:28:11+00:00

    Answer:  0.0013

    Step-by-step explanation:

    Given : The test scores are normally distributed with

    Mean : \mu=\ 60,000

    Standard deviation :\sigma= 4,000

    Sample size : n=4

    The formula to calculate the z-score :-

    z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}

    For x = 66,000

    z=\dfrac{66000-60000}{\dfrac{4000}{\sqrt{4}}}=3

    The p-value = P(z>3)\=1-P(z<3)=1- 0.9986501\approx0.0013

    Hence, the likelihood the mean tire life of these four tires is more than 66,000 miles = 0.0013

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