Answered: The annual salary for one particular…

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 annual salary for one particular occupation is normally distributed, with a mean of about

$131,000

and a standard deviation of about

$24,000.

Random samples of

are drawn from this population, and the mean of each sample is determined. Find the mean and standard deviation of the sampling distribution of these sample means. Then, sketch a graph of the sampling distribution.

The mean is

μx=nothing,

and the standard deviation is

σx=nothing.

(Round to the nearest integer as needed. Do not include the $ symbol in your answers.)

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

131,000120,000142,000Mean salary (in dollars)

A normal curve is over a horizontal axis labeled "Mean salary (in dollars)" from 120000 to 142000 in increments of 1000 and is centered on 131,000. A vertical line segment extends from the horizontal axis to the curve at 131,000. The curve is near the axis at 120000 and 142000.

131,00059,000203,000Mean salary (in dollars)

A normal curve is over a horizontal axis labeled "Mean salary (in dollars)" from 59000 to 203000 in increments of 12000 and is centered on 131,000. A vertical line segment extends from the horizontal axis to the curve at 131,000. The curve is near the axis at 59000 and 203000.

19,52817,92821,128Mean salary (in dollars)

A normal curve is over a horizontal axis labeled "Mean salary (in dollars)" from 17928 to 21128 in increments of 200 and is centered on 19,528. A vertical line segment extends from the horizontal axis to the curve at 19,528. The curve is near the axis at 17928 and 21128.

19,5288,52830,528Mean salary (in dollars)

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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