According to the Gallup Poll, 27% of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels “could be financially devastating to the U.S. healthcare system” and are a major concern to health insurance providers. According to recent studies, cholesterol levels in healthy U.S. adults average about 215 mg/dL with a standard deviation of about 30 mg/dL and are roughly normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults is taken,
a) What shape should the sampling distribution of the mean have?
b) What would the mean of the sampling distribution be?
c) What would its standard deviation be?
d) If the sample size were increased to 100, how would your answers to parts a–c change?