The Distribution of Blood cholesterol level

#1
Im really stuck on this problem could someone please help?


The distribution of blood cholesterol level in the population of young men aged 20 to 34 years is close to Normal with mean u=168 mg/dl and standard deviation = to 35 mg/dl. You measure the cholesterol level of 150 young men chosen at random and calculae the sampling mean.

A. If you did this many times, what would be the mean and the standard deviation of the distribution of the sampling means.

B. What is the probability that your sample has mean less than 165.


Thanks
 

JohnM

TS Contributor
#2
Jerry,

A.
the mean of the distribution of sampling means is the same as the population mean
the standard deviation of the sampling means is the population standard deviation divided by the square root of the sample size

B.
compute z = (x - mu)/(s/sqrt(n))
x = 165
mu = 168
s = 35
sqrt(n) = sqrt(150)

then determine the probability of getting z or less by looking it up in the standard normal distribution tables

Hope this helps,
John