In a Gallup poll, 37% of survey respondents said that, if they only had one child, they would prefer the child to be a boy. You conduct a survey of 150 randomly selected students on your campus and ﬁnd that 75 of them would prefer a boy.
(a) Approximate the probability that, in a random sample of 150 students, at least 75 would prefer a boy, assuming the true percentage is 37%.
(b) Does this result contradict the Gallup poll? Explain.