The average number of miles (in thousands) that a car's tire will function before needing replacement is 72 and the standard deviation is 18. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What distribution oi X N( b. What is the distribution of æ? ¤ ~ N( 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 73.9 and 76.9. d. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 73.9 and 76.9.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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parts b, c, and d 

The average number of miles (in thousands) that a car's tire will function before needing replacement is 72, and the standard deviation is 18. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

b. What is the distribution of \(\bar{x}\)? \(\bar{x} \sim N(\, \text{[mean]} \,, \, \text{[standard deviation]} \,)\).

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 73.9 and 76.9. [Input Box]

d. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 73.9 and 76.9. [Input Box]
Transcribed Image Text:The average number of miles (in thousands) that a car's tire will function before needing replacement is 72, and the standard deviation is 18. Suppose that 50 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. b. What is the distribution of \(\bar{x}\)? \(\bar{x} \sim N(\, \text{[mean]} \,, \, \text{[standard deviation]} \,)\). 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 73.9 and 76.9. [Input Box] d. For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 73.9 and 76.9. [Input Box]
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