A manufacturer knows that their items have a normally distributed length, with a mean of 5 inches, and standard deviation of 1.4 inches. If one item is chosen at random, what is the probability that it is less than 7.5 inches long?

A manufacturer knows that their items have a normally distributed length, with a mean of 5 inches, and standard deviation of 1.4 inches. If one item is chosen at random, what is the probability that it is less than 7.5 inches long?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.7: Probability

Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....

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Question

A manufacturer knows that their items have a normally distributed length, with a mean of 5 inches, and standard deviation of 1.4 inches.

If one item is chosen at random, what is the probability that it is less than 7.5 inches long?

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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