Due to an unhealthy lifestyle, an unbalanced diet, or a family history of high cholesterol, children may also have high cholesterol. The National Health and Nutrition Examination Survey (NHANES) claimed that the prevalence of high total cholesterol among U.S. children and adolescents was 7.4%. To test the accuracy of this claim, you collect information from a random sample of 2,000 children and adolescents’ cholesterol level and found 160 had high cholesterol.

a. Determine whether the sampling distribution is approximatly normal with the provided data.

b. Use the p-value approach at 5% significance level to justify the claim.