Question

The LDL cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean μ=120μ=120 milligrams per deciliter and the standard deviation is σ=30σ=30 milligrams per deciliter. If you choose an SRS of 25 men from this population, what is the sampling distribution of mean cholesterol level of the 25 selected men.

Select one:

a. x¯∼N(120,1.2)x¯∼N(120,1.2)

b. Couldn't decide

c. x¯∼N(120,30)x¯∼N(120,30)

d. x¯∼N(120,6)

Answer 1

The LDL cholesterol level of all men aged 20 to 34 follows normal with mean 120 milligrams per deciliter, and the standard deviation is 30 milligrams per deciliter.

Let, X be the random variable denoting the cholesterol level of a randomly selected man aged 20 to 34.

A simple random sample of 25 men between 20 to 34 is selected.

Now, X follows normal(120,30).

Now, we know that if a random variable X follows normal distribution with mean m, and standard deviation s, then, on selecting a random sample of size n, the sample mean will also follow normal distribution with mean m and standard deviation s/sqrt(n).

Here, m=120 and s=30.

and n=25.

So, the mean of the sampling distribution of the sampling mean is

=120

And the standard deviation of the sampling distribution of the sampling mean is

=30/sqrt(25)

=30/5

=6

So, the sampling distribution of mean cholesterol level of the 25 selected men, will follow a normal distribution with mean 120 and standard deviation 6.

So, the correct answer is (d) Xbar~Normal(120,6).