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 weights of people in a certain population are normally distributed with a mean of 152 lb and a standard deviation of 22 lb. Determine the sampling distribution of the mean for samples of size 2.
A)Approximately normal, mean = 152 lb, standard deviation = 11 lb
B)Approximately normal, mean = 152 lb, standard deviation = 15.56 lb
C)Normal, mean = 152 lb, standard deviation = 22 lb
D)Normal, mean = 152 lb, standard deviation = 15.56 lb

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 weights of people in a certain population are normally distributed with a mean of 152 lb and a standard deviation of 22 lb. Determine the sampling distribution of the mean for samples of size 2. 
A)Approximately normal, mean = 152 lb, standard deviation = 11 lb
B)Approximately normal, mean = 152 lb, standard deviation = 15.56 lb
C)Normal, mean = 152 lb, standard deviation = 22 lb
D)Normal, mean = 152 lb, standard deviation = 15.56 lb

Quizplus · Accepted Answer

The distribution of the sample mean $\bar{x}$ is normal because the population distribution is normal. The mean of the sampling distribution is the same as the population mean, 152 lb. The standard deviation of the sampling distribution ($\sigma_{\bar{x}}$) is the population standard deviation ($\sigma$) divided by the square root of the sample size ($n$), which is $\frac{22}{\sqrt{2}} = 15.56$ lb.

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

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