8 (10 points) The National Health and Nutrition Examination Survey of 1988-1994

Question

8 (10 points) The National Health and Nutrition Examination Survey of 1988-1994 estimated the mean serum cholesterol level for U.S females of ages 20-74 years old to be 204 mg/dl. The estimated standard deviation was 42 mg/dl. Using these estimates as the population mean and standard deviation, respectively, consider a random sample of 49 women drawn from this population. Using the central limit theorem, find the approximate probability that the average serum cholesterol level of the women, X, is greater than 195 ml/dl. llustrate and compute.

Explanation / Answer

here std error of mean=std deviation/sqrt(n)=42/sqrt(49)=6

therefore from central limit theorum and normal approximation

probability that average serum cholestrol level is greater than 195 ml/dl

=P(Xbar>195)=P(Z>(195-204)/6)=P(Z>-1.5)=1-P(Z<-1.5)=1-0.0668 =0.9332

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