40,000 miles is the warranty period for the gearbox on a certain model of automobile. In the case of such transmissions, it is well known that the life span has a normal distribution with a mean of 72,000 miles and a standard deviation of 12,000 miles. The following questions are being asked: (a) What percentage of the transmission will fail before the end of the warranty term; and (b) What percentage of the transmission will be good for more than 100,000 miles.

40,000 miles is the warranty period for the gearbox on a certain model of automobile. In the case of such transmissions, it is well known that the life span has a normal distribution with a mean of 72,000 miles and a standard deviation of 12,000 miles. The following questions are being asked: (a) What percentage of the transmission will fail before the end of the warranty term; and (b) What percentage of the transmission will be good for more than 100,000 miles.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

The following questions are being asked: (a) What percentage of the transmission will fail before the end of the warranty term; and (b) What percentage of the transmission will be good for more than 100,000 miles.

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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