Answered: Use the central limit theorem to find…

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

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution.

The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of

114

pounds and a standard deviation of

39.2

pounds. Random samples of size

are drawn from this population and the mean of each sample is determined.

μx=enter your response here

σx=enter your response here

(Round to three decimal places as needed.)

Sketch a graph of the sampling distribution. Choose the correct graph below.

9.0 -105.0123.0

A normal curve is over a horizontal x overbar axis labeled from negative 105.0 to 123.0 and is centered on 9.0.

114 87.0141.0

A normal curve is over a horizontal x overbar axis labeled from 87.0 to 141.0 and is centered on 114.

114 96.0132.0

A normal curve is over a horizontal x overbar axis labeled from 96.0 to 132.0 and is centered on 114.

9.0 -333.0351.0

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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