Answered: Find the probability that: (a) A lot…

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 hardness of a species of tree is normally distributed with a mean of 3260lb and a standard deviation of 41 lb. The trees are sold to a furniture manufacturer in lots of 30. The manufacturer, valuing the quality and consistency of the trees, rejects a lot of 30 trees if it has an average hardness below 3250 lb for a sample standard deviation above 50 lb. Find the probability that:

(a) A lot of 30 trees have average hardness below 3250lbf.

(b) A lot of 30 trees have a sample standard deviation above 50lbf.

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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