Question

Assume total cholesterol levels (TChol) are normally distributed with mean μ = 215 mg/dl and standard deviation σ = 30 mg/dl for the adult American population. That is, TChol ~ N(215, 302). Total cholesterol values of 240 mg/dl or greater are considered high; and levels in the range of 200 to 240 are called borderline high.
a. What proportion of this population do we expect to find with high cholesterol? What proportion do we expect to find with borderline high cholesterol?
Suppose that a random sample of 150 men aged 45-64 have their cholesterol checked. Forty of the men are found to have high cholesterol, and 85 of the men have borderline high levels.
b. How do the observed proportion of men with borderline high and high cholesterol compare to the expected proportions?
c. What are the expected value (mean) and standard error of total cholesterol for samples of size n=150?
d. The sample mean total cholesterol of the 150 men was xbar=220.4 mg/dl. Knowing that the sampling distribution is normal when the underlying population distribution is normal, what is the probability of observing a sample mean of 220.4 mg/dl or greater if we assume that the distribution for men in this age group is the same as the full population of American adults?

What conclusions can you draw about total cholesterol levels among men in this age group based upon your results?
Does this agree / disagree with your answer to part (b)?

Answer 1

Disagree with (b)