Answered: The head of maintenance at XYZ…

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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The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2433 miles, with a standard deviation of 332miles.

If he is correct, what is the probability that the mean of a sample of 35 cars would differ from the population mean by less than 48 miles? Round your answer to four decimal places.

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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The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 28,63128,631 miles, with a variance of 16,834,61016,834,610.

What is the probability that the sample mean would differ from the population mean by less than 219219 miles in a sample of 178178 tires if the manager is correct? Round your answer to four decimal places.

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