A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 9.6 inches, and standard deviation of 3 inches. If 30 items are chosen at random, what is the probability that their mean length is greater than 8.2 inches?

A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 9.6 inches, and standard deviation of 3 inches. If 30 items are chosen at random, what is the probability that their mean length is greater than 8.2 inches?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 10E

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Question

A manufacturer knows that their items have a lengths that are approximately normally distributed, with a mean of 9.6 inches, and standard deviation of 3 inches.

If 30 items are chosen at random, what is the probability that their mean length is greater than 8.2 inches?

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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