The previous study indicated that several factors may be risk factors for premature delivery, among them a high basal metabolic index (BMI) in the mother. Suppose BMI at 20 weeks' gestation has a mean of µ=28.5 with a standard deviation of σ=3.6.
A. Suppose the obstetrician will see 74 pregnant women over the next week; how many of them will have BMI between 25 and 30? (½ mark)
B. Suppose we collect a sample of 100 pregnant women from a different antenatal care clinic, what is the probability that the sample mean for that sample is within 1 unit of the true BMI, if the standard deviation for BMI is 3.6?