A market research firm conducts telephone surveys with a 46% historical response rate.

a. What is the probability that in a new sample of 400 telephone numbers, at least 160 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 160/400 = 0.4?

Calculate the standard error to 4 decimals.

Calculate the probability to 4 decimals, showing your steps along the way

b. If a follow-up study was completed a year later with only 64 telephone numbers, what is the probability that the response rate was between 42% and 48%?

Calculate the standard error to 4 decimals.

Calculate the probability to 4 decimals, showing your steps along the way.