Answered: A random variable is not normally…

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

A random variable is not normally distributed, but it is mound shaped. It has a mean of 18 and a standard deviation of 2.

If you take a sample of size 12, can you say what the shape of the sampling distribution for the sample mean is? Why?

If the sample size is 12, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is less than 30.
If the sample size is 12, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is less than 30.
If the sample size is 12, then you can say the sampling distribution of the sample mean is normally distributed since the sample size is less than 30.

For a sample of size 12, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary.
μ_x̄ =
σ_x̄ =

If you take a sample of size 36, can you say what the shape of the distribution of the sample mean is? Why?

If the sample size is 36, then you can say the sampling distribution of the sample mean is not normally distributed since the sample size is greater than 30.
If the sample size is 36, then you can say the sampling distribution of the sample mean is normally distributed since the sample size is greater than 30.
If the sample size is 36, then you can't say anything about the sampling distribution of the sample mean, since the population of the random variable is not normally distributed and the sample size is greater than 30.

For a sample of size 36, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary.
μ_x̄ =
σ_x̄ =

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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