Question

According to a recent​ poll,

26​%

of adults in a certain area have high levels of cholesterol. They report that such elevated levels​ "could be financially devastating to the regions healthcare​ system" and are a major concern to health insurance providers. Assume the standard deviation from the recent studies is accurate and known. According to recent​ studies, cholesterol levels in healthy adults from the area average about 205 ​mg/dL, with a standard deviation of about 35​mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of 41 healthy adults from the region is​ taken, answer parts ​(a) through ​(d).

​(a) What is the probability that the mean cholesterol level of the sample will be no more than 205​?

(b) 200 and 210​?

(c) 195​?

(d) 217​?

Answer 1

For the sample size of 41 adults, the distribution of the sample mean is obtained here as:

a) The probability that the mean cholesterol level of the sample will be no more than 205​ is computed here to be 0.5 because the normal distribution is symmetrical about its mean. Therefore 0.5 is the required probability here.

b) The probability here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.6396 is the required probability here.

c) The probability here is computed as:

Converting it to a standard normal variable, we get here:

Getting it from the standard normal tables, we get here:

Therefore 0.0337 is the required probability here.

d) The probability here is computed here as:

Getting it from the standard normal tables, we get here:

Therefore 0.9859 is the required probability here.