Identify the distribution of the sample mean. In particular, state whether the distribution of $\bar { x }$ is normal or approximately normal and give its mean and standard deviation.
-The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5700. The distribution of incomes is skewed to the right. Determine the sampling
Distribution of the mean for samples of size 132.
A)Approximately normal, mean = $28,520, standard deviation = $5700
B)Normal, mean = $28,520, standard deviation = $43
C)Approximately normal, mean = $28,520, standard deviation = $496
D)Normal, mean = $28,520, standard deviation = $496

Question

Identify the distribution of the sample mean. In particular, state whether the distribution of $\bar { x }$ is normal or approximately normal and give its mean and standard deviation.
-The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5700. The distribution of incomes is skewed to the right. Determine the sampling
Distribution of the mean for samples of size 132. 
A)Approximately normal, mean = $28,520, standard deviation = $5700
B)Normal, mean = $28,520, standard deviation = $43
C)Approximately normal, mean = $28,520, standard deviation = $496
D)Normal, mean = $28,520, standard deviation = $496

Quizplus · Accepted Answer

The distribution of the sample mean ($\bar{x}$) will be approximately normal due to the Central Limit Theorem, given the sample size is large (n=132). The mean of the sampling distribution is equal to the population mean ($28,520). The standard deviation of the sampling distribution ($\sigma_{\bar{x}}$) is the population standard deviation ($5700) divided by the square root of the sample size ($\sqrt{132}$), which calculates to approximately $496.

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

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