Answered: A variable of a population has a mean…

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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A variable of a population has a mean of μ=86 and a standard deviation of σ=7.

a. Identify the sampling distribution of the sample mean for samples of size 49.

b. In answering part (a), what assumptions did you make about the distribution of the variable?

c. Can you answer part (a) if the sample size is 16 instead of 49? Why or why not?

a. What is the shape of the sampling distribution?

bimodal

normal

skewed

uniform

What is the mean of the sampling distribution?

μx=_________________

(Simplify your answer.)

What is the standard deviation of the sampling distribution?

σx=____________________

(Simplify your answer)

b. In answering part (a), what assumptions did you make about the distribution of the variable?

A. It was assumed that the distribution of the variable was unimodal.

B. No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration.

C. It was assumed that the variable was normally distributed.

D. No assumptions were made because the sampling distribution is normal, regardless of the distribution of the variable under consideration.

c. Can you answer part (a) if the sample size is 16 instead of 49?
Why or why not?

A. No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.

B. No, because the sample size must be less than 5 if the distribution of the variable is unknown.

C. Yes, because the sample size must be less than 30 if the distribution of the variable is unknown.

D. Yes, because the sample size makes no difference in determining the sampling distribution.

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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