Identify the distribution of the sample mean. In particular, state whether the distribution of $\bar { x }$ is normal or approximatelynormal and give its mean and standard deviation.
-The heights of people in a certain population are normally distributed with a mean of 65 inches and a standard deviation of 3.9 inches. Determine the sampling distribution of the mean for samples of Size 44.
A)Normal, mean = 65 inches, standard deviation = 0.59 inches
B)Approximately normal, mean = 65 inches, standard deviation = 0.09 inches
C)Normal, mean = 65 inches, standard deviation = 3.9 inches
D)Normal, mean = 65 inches, standard deviation = 0.09 inches

Question

Identify the distribution of the sample mean. In particular, state whether the distribution of $\bar { x }$ is normal or approximatelynormal and give its mean and standard deviation.
-The heights of people in a certain population are normally distributed with a mean of 65 inches and a standard deviation of 3.9 inches. Determine the sampling distribution of the mean for samples of Size 44. 
A)Normal, mean = 65 inches, standard deviation = 0.59 inches
B)Approximately normal, mean = 65 inches, standard deviation = 0.09 inches
C)Normal, mean = 65 inches, standard deviation = 3.9 inches
D)Normal, mean = 65 inches, standard deviation = 0.09 inches

Quizplus · Accepted Answer

The original population is normally distributed, so the sampling distribution of the mean will also be normal regardless of sample size. The mean of the sampling distribution is the same as the population mean (65 inches). The standard deviation of the sampling distribution (standard error) is the population standard deviation (3.9 inches) divided by the square root of the sample size (44), which is approximately 0.59 inches.

Identify the Distribution of the Sample Mean xˉ\bar { x }xˉ

Identify the Distribution of the Sample Mean $\bar { x }$