Suppose that in a certain population of adult males, the variable x = "total serum cholesterol level (mg/dl)" is found to be normally distributed, with mean = 220 and standard deviation = 40.(a) suppose that a random sample of n = 36 males is to be selected from this population, and the sample mean cholesterol level calculated. what is the probability that this sample mean value is between 202 and 238? (b) how large a sample size n is necessary to guarantee that 80% of the sample mean values are within 5 mg/dl of the mean of their distribution? (hint: first find the value of z that satisfies p(? z ? z ? +z) = 0.8, then change back to x, and solve for n.)