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 170 randomly selected students on your...

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 170 randomly selected students on your campus and find that 84
of them would prefer a boy.

​(a) Use the normal approximation to the binomial to approximate the probability​ that, in a random sample of 170​students, at least 84
would prefer a​ boy, assuming the true percentage is 45​%.

​(b) Does this result contradict the​ poll? Explain.