Question

According to a recent poll cholesterol levels in healthy adults are skewed right with a mean of 209 mg/dL and a standard deviation of 35 mg/dL. A random sample of 42 healthy adults is selected. Find the probability that the total cholesterol level in the sample of 42 adults will be less than 8400.

a. 0.0475

b. 0.9525

c. 1

d. 0

e. 0.3974

Answer 1

Solution:

Given that ,

= 209

= 35

A sample of size n = 42 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 209

SD =      = 35/​42 =   5.400617

Now,

P[sum of sample is less than 8400]

=P[sample mean is less than 8400/42]

= P[ < 200]

= P[( - )/ < (200 - 209)/5.400617]

= P[Z < -1.67]

= 0.0475