Assume that there is a mayoral election coming up in a certain city and 40% of the voters in the city support a certain candidate. A sample of 500 voters is polled, and the the proportion p , of voters who approve of the candidate is calculated.

a) Find the mean p and standard deviation p of the sample proportion .

b) Find the probability that the sample proportion is between 0.38 and 0.42.

c) Find the probability that the sample proportion is between 0.36 and 0.44.

d) Find the probability that the sample proportion is between 0.34 and 0.46.