Researchers have calculated that if at least 100 individuals respond to their provincial-wide survey distributed by mail, the sample size will be large enough to draw further conclusions. It is known from experience that only 70% of those who receive a survey return their answers to researchers. For this reason, researchers have decided to send a questionnaire for a total of 150 people. Researchers assume that each person answers or fails to respond independently of the others.

A) Using a binomial distribution, calculate (without normal approximation) the probability that that researchers receive exactly x answers to their questionnaire, with x values of 100, 101, and 130.

B) Determine an estimate of the probability (using the normal approximation!) with which the researchers receive at least 100 responses to their survey