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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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Answer:

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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