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 190 randomly selected students on your campus and find that 86 of them would prefer a boy.
a) Use the normal approximation to the binomial to approximate the probability that, in a random sample of 190 students, at least 86 would prefer a boy, assuming the true percentage is 45%.
b) Does this result contradict the poll? Explain