Question

The distribution of blood cholesterol level in the

Answer 1

Answer: A. Mean of sampling means $=\mu=168\ Mg/dl$

Standard deviation of sampling means =$2.86\ mg/dl$

B. The probability that your sample has mean less than  165 is 0.1492 .

Given : The distribution of blood cholesterol level in the

population of young men aged 20 to 34 years is close to normal with

mean $\mu= 168$ Mg/dl and standard deviation $\sigma= 35$ mg/dl.

Sample size : n= 150

Let $\overline{x}$ sample mean values.

A. The mean and the  standard deviation of the distribution of the sampling means would be :

Mean of sampling means =$\mu=168\ Mg/dl$

Standard deviation of sampling means = $\dfrac{\sigma}{\sqrt{n}}=\dfrac{35}{\sqrt{150}}$

$=\dfrac{35}{12.2474487}\\\\=2.85773803649\approx2.86\ mg/dl$

The probability that your sample has mean less than  165 would be

$P(\overline{x}$

Hence , the probability that your sample has mean less than  165 is 0.1492 .