Question

A random variable is not normally distributed, but it is mound shaped. It has a mean of 17 and a standard deviation of 5.

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 the sample size is 13, 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 13, 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 13, 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 13, 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'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 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.

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 =

Answer 1

If you take a sample of size 13, the shape is: If the sample size is 13, 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 you take a sample of size 36, the shape is: 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.