A random variable is normally distributed. It has a mean of 283 and a standard deviation of 26. If you take a sample of size 11, can you say what the shape of the sampling distribution for the sample mean is? Why? If the sample size is 11, 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 11, 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 11, 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 11, 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 11, find the probability that the sample mean is more than 276. P(x̄ > 276) = If you take a sample of size 39, can you say what the shape of the distribution of the sample mean is? Why? If the sample size is 39, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed. If the sample size is 39, 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 39, 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 39, 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 39, find the probability that the sample mean is more than 276.P(x̄ > 276) =

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 normally distributed. It has a mean of 283 and a standard deviation of 26.

If you take a sample of size 11, can you say what the shape of the sampling distribution for the sample mean is? Why?

If the sample size is 11, 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 11, 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 11, 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 11, 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 11, find the probability that the sample mean is more than 276.
P(x̄ > 276) =

If you take a sample of size 39, can you say what the shape of the distribution of the sample mean is? Why?

If the sample size is 39, then you can say the sampling distribution of the sample mean is normally distributed since the variable is normally distributed.
If the sample size is 39, 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 39, 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 39, 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 39, find the probability that the sample mean is more than 276.P(x̄ > 276) =

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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