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)

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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