Answered: The annual salary for one particular occupation is normally distributed, with a mean of about $132,000 and a standard deviation of about $24,000.

MATLAB: An Introduction with Applications

6th Edition

ISBN: 9781119256830

Author: Amos Gilat

Publisher: John Wiley & Sons Inc

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

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

$132,000

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.

132,000117,000147,000Mean salary (in dollars)

A normal curve is over a horizontal axis labeled "Mean salary (in dollars)" from 117000 to 147000 in increments of 1000 and is centered on 132,000. A vertical line segment extends from the horizontal axis to the curve at 132,000. The curve is near the axis at 117000 and 147000.

132,00060,000204,000Mean salary (in dollars)

A normal curve is over a horizontal axis labeled "Mean salary (in dollars)" from 60000 to 204000 in increments of 12000 and is centered on 132,000. A vertical line segment extends from the horizontal axis to the curve at 132,000. The curve is near the axis at 60000 and 204000.

25,88723,08728,687Mean salary (in dollars)

A normal curve is over a horizontal axis labeled "Mean salary (in dollars)" from 23087 to 28687 in increments of 200 and is centered on 25,887. A vertical line segment extends from the horizontal axis to the curve at 25,887. The curve is near the axis at 23087 and 28687.

25,88710,88740,887Mean salary (in dollars)

A normal curve is over a horizontal axis labeled "Mean salary (in dollars)" from 10887 to 40887 in increments of 1000 and is centered on 25,887. A vertical line segment extends from the horizontal axis to the curve at 25,887. The curve is near the axis at 10887 and 40887.

Click to select your answer(s).

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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The annual salary for one particular occupation is normally​ distributed, with a mean of about ​$132,000 and a standard deviation of about ​$24,000.

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The annual salary for one particular occupation is normally distributed, with a mean of about $132,000 and a standard deviation of about $24,000.