What is the probability that at least 76 students would prefer a boy?

Question

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 140 randomly selected students on your campus and find that 76 of them would prefer a boy.

Use the normal approximation to the binomial to approximate the probability​ that, in a random sample of 140​students, at least 76 would prefer a​ boy, assuming the true percentage is 45​%.

The probability that at least 76 students would prefer a boy is?

Answer 1

Binomial distribution: μ = np = 140* .45 = 63

σ = sqrt(np(1-p)) = 5.886

Treat as normal distribution (ok for np > 10 and n(1-p) >10), so find z for condition:

z = (76 - 63)/ 5.886 = 2.209

We want to find the right tail area for z = 2.209 -> 1 - .989 = .011

Hope that helps.