Awarding of home improvement grants. A community development agency makes home improvement grants each year to homeowners in depressed city neighborhoods. One year, grants were awarded by the city council via a “random selection”

of 142 homeowners’ applications from among a total of 750 applications: 603 from the north side, and 147 from the south side, of the city. Oddly, all 142 grants awarded were from the north side—clearly a highly improbable outcome if, in fact, the 142 winners were randomly selected from among the 750 applicants.

a. Suppose the 142 winning applications were randomly selected from among the total of 750, and let x equal the number in the sample from the north side. Find the mean and standard deviation of x.

b. Use the results of part a to support a contention that the grant winners were not randomly selected.