# According to one study, brain weights of men are normally distributed with a mean of 1.20kg and a standard deviation of 0.13kg. Use the data to answer

According to one​ study, brain weights of men are normally distributed with a mean of 1.20kg and a standard deviation of 0.13kg. Use the data to answer questions​ (a) through​ (e). a. Determine the sampling distribution of the sample mean for samples of size 3. The mean of the sample mean is $\mu x=?$ The standard deviation of the sample mean is $\sigma x=?$ ​(Round to four decimal places as​ needed.) b. Determine the sampling distribution of the sample mean for samples of size 12. The mean of the sample mean is $\mu x=?$ The standard deviation of the sample mean is $\sigma x=?$ (Round to four decimal places as​ needed.)
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Given:

$\mu =1.20kg$
$\sigma =0.13kg$

a) Given: $n=3$

The mean of the sample mean is ${\mu }_{x}=\mu =1.20$

The standard deviation of the sample mean is ${\sigma }_{x}=\frac{\sigma }{\sqrt{n}}=\frac{0.13}{\sqrt{3}}=0.0751$

b) Given: $n=12$

The mean of the sample mean is ${\mu }_{x}=\mu =1.20$

The standard deviation of the sample mean is ${\sigma }_{x}=\frac{\sigma }{\sqrt{n}}=\frac{0.13}{\sqrt{12}}=0.0375$