According to a recent poll, 29% 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 have a mean of 206mg/dL, with a standard deviation of 30mg/dL, and are roughly Normally distributed. If the cholesterol levels of a sample of 50 healthy adults from the region is taken, answer parts (a) through (d).
(a) What is the probability that the mean cholesterol level of the sample will be no more than 206? P(ybar < or equals206)= __(Round to four decimal places as needed.)
(b) What is the probability that the mean cholesterol level of the sample will be between 201 and 211? P(201 < ybar < y bar < 211) = __(Round to four decimal places as needed.)
(c) What is the probability that the mean cholesterol level of the sample will be less than 196? P(ybar<196) = __(Round to four decimal places as needed.)
(d) What is the probability that the mean cholesterol level of the sample will be greater than 218?