The lengths of lumber a machine cuts are normally distributed with a mean of101inches and a standard deviation of0.5inch.(a) What is the probability that a randomly selected board cut by the machine has a length greater than101.17inches?(b) A sample of41boards is randomly selected. What is the probability that their mean length is greater than101.17inches? (a) The probability is ____.(Round to four decimal places as needed.)(b) The probability is ____.(Round to four decimal places as needed.)

Given data Normal distribution Mean = 101 inches Standard deviation = 0.5 inches

Answered: The lengths of lumber a machine cuts…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The lengths of lumber a machine cuts are normally distributed with a mean of

101

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

101.17

inches?

(b) A sample of

boards is randomly selected. What is the probability that their mean length is greater than

101.17

inches?

(a) The probability is ____.

(Round to four decimal places as needed.)

(b) The probability is ____.

(Round to four decimal places as needed.)

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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