According to a recent poll, 26% of adults in a certain area have high levels of

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. According to recent studies, cholesterol levels in healthy adults from the area average about 208 mg/dL, with a standard deviation of about 30 mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of 49 healthy adults from the region is taker, answer parts (a) through (d). (a) What is the probability that the mean cholesterol level of the sample will be no more than 208? P(y lessthanorequalto 208) = .5000 (b) What is the probability that the mean cholesterol level of the sample will be between 203 and 213? P(203

Explanation / Answer

mean = 208 , s = 30 , n = 49

a) P (203 < x <213)

z =( x -mean) /( s /sqrt(n))
= ( 203 - 208 ) / ( 30 / sqrt(49))
= -1.167

P(X < 213)

z =( x -mean) /( s /sqrt(n))
= ( 213 - 208 ) / ( 30 / sqrt(49))
= 1.167

P(203 < x <213) = P ( -1.167 < z < 1.167) = 0.7566

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