Question

According to a recent​ poll, 27​% 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 30​mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of 45 healthy adults from the region is​ taken, answer parts ​(a) through ​(d)..

(b) What is the probability that the mean cholesterol level of the sample will be between 200 and 210​?

​P(200 < y <210​ ) = [ ] ​(Round to three decimal places as​ needed.)

Answer 1

= 205

= 30

n = 45

SE = /

= 30/ = 4.4721

To find P(200 < < 210):

Case 1: For from 200 to mid value:

Z = (200 - 205)/4.4721 = - 1.1180

Table of Area Under Standard Normal Curve gives area = 0.3686

Case 2: For from mid value to 210:

Z = (210 - 205)/4.4721 = -1.1180

Table of Area Under Standard Normal Curve gives area = 0.3686

So,

P(200 < <210) = 0.3686 X 2 = 0.7372

So,

Answer is:

0.737