Answered: A car company has found that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A car company has found that the lifetime of its disc brake pads varies from car to car according to a Normal Distribution with mean μ = 55,000 miles and a standard deviation σ = 4500 miles. The company installs a new brand of brake pads on an SRS of 8 cars.

a. If the new brand has the same lifetime distribution as the previous type of brake pad, describe the sampling distribution of the mean lifetime x.

Shape:

Mean:

Standard deviation:

b. The average life of the pads on these 8 cars turns out to be x 51,800 miles. Find the probability that the sample mean lifetime is 51,800 miles or less if the lifetime distribution is unchanged.

c. Using your answer from part (b), would you conclude that the new brake pads have the same distribution as the old brake pads? Explain your reasoning.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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