In 2006-2007, the Canadian in-hospital preterm birth (prematurity, that is, birth before 37 weeks of gestation) and SGA (small for their gestational age) rates were approximately 8.1% and 8.3%, respectively, accounting for more than 54,000 live births combined. Among the provinces, Alberta and Newfoundland and Labrador demonstrated the highest preterm birth rates, at 8.7% and 8.6%, respectively. The highest provincial SGA rates occurred in Ontario (8.9%) and Alberta (8.7%).

a. Suppose a random sample of 25 live births is taken in Newfoundland and Labrador. Would the normal approximation for some probability calculation for preterm birth be appropriate here? Why or why not?

b. Based on this information, what is the expected number of SGA births if we randomly sample 200 births in Alberta?

c. What is the approximate probability of 60 or more SGA births from a random sample of 200 in Ontario?

d. If a survey of 500 randomly selected Canadian in-hospital births is conducted, what is the approximate probability that at most 50 of these births will be declared SGA? Further, what is the probability that more than 10% of the sampled births will be termed SGA?

e. Suppose a survey of 25 randomly selected Canadian in-hospital births is conducted. Calculate the exact and approximate probability that at least one of these births will be termed SGA. Compare the results. How close or far was your approximation? Explain.