Question

BACKGROUND: The Saint Clair River connects the upper Great Lakes with the lower ones, and is called “Chemical Valley” due to the heavy concentration of petrochemical facilities. (Approximately ½ of all of Canada’s petrochemical production comes from this area.) The Canadian health authorities have concluded that this area has an extreme gender imbalance, as only 34.8% of newborns in the area are male.

(a) For the province of Ontario overall, 51.1% of all babies born are male. Based on this value, if 200 random Ontarians are selected, 102 will be male (p=0.51). If 20 of these 200 are selected, what is the probability of exactly 7 being male, using both a binomial and a hypergeometric distribution? What is your conclusion about this?

(b) One of the problems that Sarnia, Ontario (the heart of “Chemical Valley”) is having as a result of this gender imbalance is difficulty in fielding all-male sports teams. Suppose 70 players are available for the local hockey teams. What is the probability of having enough players for the boys’ team if 5 are required (i.e. 5 or more)? If 10 are required (10 or more)? [Use both the binomial and hypergeometric distributions.]

Answer 1