Awarding of home improvement grants. A curious event was described in the Minneapolis Star and Tribune . The Minneapolis Community Development Agency (MCDA) makes home improvement grants each year to homeowners in depressed city neighborhoods. Of the $708,000 granted one year, $233,000 was awarded by the city council via a “random selection” of 140 homeowners’ applications from among a total of 743 applications: 601 from the north side, and 142 from the south side, of Minneapolis. Oddly, all 140 grants awarded were from the north side—clearly a highly improbable outcome if, in fact, the 140 winners were randomly selected from among the 743 applicants.
a. Suppose the 140 winning applications were randomly selected from among the total of 743, 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.
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