# The average number of miles (in thousands) that a car's tire will function beforeneeding replacement is 68 and the standard deviation is 12. Suppose that 6randomly selected tires are tested. Round all answers to 4 decimal places wherepossible and assume a normal distribution.a. What is the distribution of X? X~ N(b. What is the distribution of T?~ N(c. If a randomly selected individual tire is tested, find the probability that thenumber of miles (in thousands) before it will need replacement is between64.8 and 71.7.d. For the 6 tires tested, find the probability that the average miles (inthousands) before need of replacement is between 64.8 and 71.7.

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Step 1

Given data

Mean = 68

Standard deviation = 12

As per binomial approximation

Mean = np > 5 and standard deviation = npq > 5

So it will follow normal distribution

a) The distribution of x is Normal i.e. X ~ N(68,122)

b) The distribution of x-bar is

Step 2

c)

If the randomly selected individual tire is tested, probability that the number of miles before it will need replacement is between 64.8 and 71.7 is given by

Step 3

d)

For the 6 tires tested, probability that the average miles before...

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