In a recent poll, 45% of survey respondents said that, if they only had one child, they would prefer the child to be a boy. Suppose you conducted a survey of 130 randomly selected students on your campus and find that 72 of them would prefer a boy.

Required:
a. Use the normal approximation to the binomial to approximate the probability that, in a random sample of 150 students, at least 82 would prefer a boy, assuming the true percentage is 46%.
b. Does this result contradict the poll? Explain.