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 ?

i looked all over to find the answer while i was being tested (yes i cheated, but its because the teacher gave us this as a surprise test becasue 1 kid was being disruptive...) anyways idk the answers are correct but this is what i did. i couldn/t find an answer anywhere. only chegg had an answer but they cost like $20 a month. sorry i was time limited so my handwritting is really bad. enjoy and make corrections if im wrong... Good luck!