The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 13. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X N( 65 13 b. What is the distribution of ? N( 65 c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 64.2 and 66.8. d. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 64.2 and 66.8. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes

Question

Answer C D and E 

The average number of miles (in thousands) that a car's tire will function before needing replacement is 65
and the standard deviation is 13. Suppose that 50 randomly selected tires are tested. Round all answers to
4 decimal places where possible and assume a normal distribution.
a. What is the distribution of X? X N( 65
13
b. What is the distribution of ? N( 65
c. If a randomly selected individual tire is tested, find the probability that the number of miles (in
thousands) before it will need replacement is between 64.2 and 66.8.
d. For the 50 tires tested, find the probability that the average miles (in thousands) before need of
replacement is between 64.2 and 66.8.
e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes
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Transcribed Image Text

The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 13. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X N( 65 13 b. What is the distribution of ? N( 65 c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 64.2 and 66.8. d. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 64.2 and 66.8. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes

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