A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 500 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.47.

(a) What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 ?

The polling agency will take another sample from a different region, Region B, of the city. The agency plans to select a random sample of 400 voters. Assume that the population proportion of voters who would support the ballot measure in Region B is 0.51.

(b) Describe the sampling distribution of the difference in sample proportions (Region B minus Region A).
(c) What is the probability that the two sample proportions will differ by more than 0.05 ?