The lifetimes of the tread of a certain automobile tire are normally distributed with mean of 45,000 miles and a standard deviation of 3,000 miles.For each of the questions below make sure to show your work. Round any z-score calculated to two decimal places to find your result.What percent of tires have a tread life between 39,000 and 51,000 miles?The manufacturer wants to know what percent of times tread life is less than 37,500 miles.Find the tread life for the 90th percentile. Round to nearest integer (if needed)

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Description: The lifetimes of the tread of a certain automobile tire are normally distributed with mean of 45,000 miles and a standard deviation of 3,000 miles.For each of the questions below make sure to show your work. Round any z-score calculated to two decima

1. The percent of tires have a tread life between 39,000 and 51,000 miles is obtained below: From the given information, the value of mean is 45,000 miles and standard deviation is 3,000 miles. The required formula is given below: The required value is given below: In percentage = 0.9546 × 100% = 95.46% Thus, the percent of tires have a tread life between 39,000 and 51,000 miles is 95.46%.2. The percent of times tread life is less than 37,500 miles is obtained below: The required value is given below: In percentage = 0.0062 × 100% = 0.62% Thus, the percent of times tread life is less than 37,500 miles is 0.62%.3. The 90th percentile for the tread life is obtained below: The 90th percentile for the weight of seedless watermelons consider is P (Z≤z) = 0.90 From the standard normal table, locate the probability value of 0.90. Move to z until the first column is reached. Note the value as 1.2 Move upward until the top row is reached. Note the value as 0.08. The intersection of the row and column values gives the area to the two tail of z as 1.28. That is P (Z≤1.28) = 0.90.. The required value is, Thus, the 90th percentile for the tread life is 48,840.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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The lifetimes of the tread of a certain automobile tire are normally distributed with mean of 45,000 miles and a standard deviation of 3,000 miles.

For each of the questions below make sure to show your work. Round any z-score calculated to two decimal places to find your result.

What percent of tires have a tread life between 39,000 and 51,000 miles?
The manufacturer wants to know what percent of times tread life is less than 37,500 miles.
Find the tread life for the 90th percentile. Round to nearest integer (if needed)

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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