Answered: A machine that produces ball bearings…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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Question

A machine that produces ball bearings has
initially been set so that the true average diameter of the
bearings it produces is 0.500 inches. A bearing is acceptable
if its diameter is within 0.004 inches of this target value.
Suppose, however, that the setting has changed during the
course of production, so that the distribution of the diameters
produced is well approximated by a normal distribution with
mean 0.499 inches and standard deviation 0.002 inches.
What percentage of the bearings produced will not be
acceptable?

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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