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26 April, 19:32

The top-selling Red and Voss tire is rated 70000 miles, which means nothing. In fact, the distance the tires can run until wear-out is a normally distributed random variable with a mean of 79000 miles and a standard deviation of 5000 miles. A. What is the probability that the tire wears out before 70000 miles? Probability = 0.0539 B. What is the probability that a tire lasts more than 83000 miles? Probability =

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  1. 26 April, 19:53
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    Step-by-step explanation:

    The distance the tyres can run until wear-out is a normally distributed, the formula for normal distribution is expressed as

    z = (x - u) / s

    Where

    x = the distance the tyres can run until wear-out

    u = mean distance

    s = standard deviation

    From the information given,

    u = 7900 miles

    s = 5000 miles

    A) We want to find the probability probability that the tyre wears out before 70000 miles. It is expressed as

    P (x lesser than 70000)

    For x = 70000,

    z = (70000 - 79000) / 5000 = - 1.8

    Looking at the normal distribution table, the corresponding z score is 0.03593

    B) We want to find the probability probability that the tyre lasts more than 83000 miles. It is expressed as

    P (x greater than 83000) = 1 - P (x lesser than or equal to 83000)

    For x = 83000,

    z = (83000 - 79000) / 5000 = 0.8

    Looking at the normal distribution table, the corresponding z score is 0.78814

    P (x greater than 83000)

    = 1 - 0.78814 = 0.21
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