The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 14. Suppose that 48 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.What is the distribution of XX? XX ~ N(Correct,) What is the distribution of ¯xx¯? ¯xx¯ ~ N(Correct,) 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 65.7 and 67.1.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 25SGR

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The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 14. Suppose that 48 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution.

What is the distribution of XX? XX ~ N(Correct,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(Correct,)
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 65.7 and 67.1.

Expert Solution

Step 1

Let X be the number of miles (in thousands) that a car's tire will function before needing replacement.

The average number of miles (in thousands) that a car's tire will function before needing replacement is 65 and the standard deviation is 14.

The following information about the mean and standard deviation has been provided:

μ=65, σ=14

It is asked

What is the distribution of XX? XX ~ N(Correct,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(Correct,)
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 65.7 and 67.1

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