A random variable is normally distributed. It has a mean of 249 and a standard deviation of 22.If you take a sample of size 13, can you say what the shape of the sampling distribution for the sample mean is? Why?If you take a sample of size 40, can you say what the shape of the distribution of the sample mean is? Why?If the sample size is 40, 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.If the sample size is 40, 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 40, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed. For a sample of size 40, state the mean of the sample mean and the standard deviation of the sample mean. Round to two decimal places if necessary.μx̄ = σx̄ = For a sample of size 40, find the probability that the sample mean is more than 245.P(x̄ > 245) =

If the sample size is 13, then you can say the sampling distribution of the sample mean is normally…

Answered: A random variable is 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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A random variable is normally distributed. It has a mean of 249 and a standard deviation of 22.

If you take a sample of size 13, can you say what the shape of the sampling distribution for the sample mean is? Why?

If you take a sample of size 40, can you say what the shape of the distribution of the sample mean is? Why?

If the sample size is 40, 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.
If the sample size is 40, 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 40, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed.

For a sample of size 40, 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 =

For a sample of size 40, find the probability that the sample mean is more than 245.P(x̄ > 245) =

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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