According to the most recent Labor Department data 105 of en

According to the most recent Labor Department data, 10.5% of engineers (electrical, mechanical, civil, and industrial) were women. Suppose a random sample of 50 engineers is selected. How likely is it that the random sample of 50 engineers will contain 8 or more women in these positions?

Solution

mean=n*p=50*0.105 =5.25

standard deviation = sqrt(n*p*(1-p)) =sqrt(50*0.105*(1-0.105)) =2.16766

So the probability is

P(X>=8) = P((X-mean)/s >(8-5.25)/2.16766)

=P(Z>1.27) =0.1020 (from standard normal table)

Answer: 0.1020