Answered: uppose that the lifetimes of tires of a…

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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Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 75,000 miles and a standard deviation of σ miles. These tires come with a 65,000-mile warranty. The manufacturer of the tires can adjust

σ during the production process, but the adjustment of σ is quite costly. The manufacturer wants to set σ once and for all so that only 10% of the tires will fail before warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

Transcribed Image Text:**Problem: Tire Lifetimes and Standard Deviation** Suppose that the lifetimes of tires of a certain brand are normally distributed with a mean of 75,000 miles and a standard deviation of σ miles. These tires come with a 65,000-mile warranty. The manufacturer of the tires can adjust σ during the production process, but the adjustment of σ is quite costly. The manufacturer wants to set σ once and for all so that only 10% of the tires will fail before the warranty expires. Find the standard deviation to be set. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place. **Diagram/Graph Explanation:** There is a small input box for entering the number of miles, with options to clear the input (an 'X' button), reset (a circular arrow button), and get help (a question mark button).

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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