The average number of miles (in thousands) that a car's tire will function before needing replacement is 71 and the standard deviation is 16. Suppose that 43 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(,)What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)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 68.8 and 71.For the 43 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 68.8 and 71.For part d), is the assumption that the distribution is normal necessary? NoYes

Answered: What is the distribution of XX? XX ~…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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The average number of miles (in thousands) that a car's tire will function before needing replacement is 71 and the standard deviation is 16. Suppose that 43 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(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
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 68.8 and 71.
For the 43 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 68.8 and 71.
For part d), is the assumption that the distribution is normal necessary? NoYes

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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