The lengths of lumber a machine cuts are normally distributed with a mean of 86 inches and a standard deviation of 0.5 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 86.15 inches? (b) A sample of 44 boards is randomly selected. What is the probability that their mean length is greater than 86.15 inches?

The lengths of lumber a machine cuts are normally distributed with a mean of 86 inches and a standard deviation of 0.5 inch. (a) What is the probability that a randomly selected board cut by the machine has a length greater than 86.15 inches? (b) A sample of 44 boards is randomly selected. What is the probability that their mean length is greater than 86.15 inches?

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

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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