Answered: The town of KnowWearSpatial, U.S.A.…

Name: The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal
Uploaded: 2024-03-20T07:07:12.000Z
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Description: The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4853 households discard waste with weights having a mean that exceeds 26.54 lb/wk. For many different weeks, it is found that the samples of 4853

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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The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4853 households discard waste with weights having a mean that exceeds 26.54 lb/wk. For many different weeks, it is found that the samples of 4853 households have weights that are normally distributed with a mean of 26.17 lb and a standard deviation of 12.24 lb. What is the proportion of weeks in which the waste disposal facility is overloaded? P(M > 26.54) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

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.

Expert Solution

Step 1

$\mathbf{Solution}$

$\mathbf{given:}$

$\mathrm{Population\;mean\;(\mu)=26.17 }$

$\mathrm{Population\;standard\; deviation\;(\sigma)=12.24}$

$\mathrm{Sample\;size\;(n)=4853}$

$\mathbf{formula:}$

$\mathrm{Z=\frac{M-\mu}{\frac{\sigma }{\sqrt{n}}}}$

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