Assume 42 of us have Group O blood A hospital is conducting

Assume 42% of us have Group O blood. A hospital is conducting a blood drive because its supply of Group O blood is low, and it needs at least 159 donors of Group O blood. If 392 volunteers donate blood, estimate the probability that the number with Group O blood is at least 159. Is the pool of 392 volunteers likely to be sufficient?

Please provide an explanation as to how your got your answer as I will not select the best answer or provide points until there is a detailed explanation given with the answers. Thank you!

Solution

Since n*p and n*(1-p) are greater than 10, we can use normal distribution approximated.

mean=n*p=392*0.42=164.64

standard deviation =sqrt(n*p*(1-p)) =sqrt(392*0.42*(1-0.42)) =9.77196

So the probability that the number with Group O blood is at least 159 is

P(X>159) = P((X-mean)/s >(159-164.64)/9.77196)

=P(Z>-0.58) =0.7190 (from standard normal table)

Yes, the pool of 392 volunteers is likely to be sufficient becase we can use normal distribution approximated.