Question

According to the laws of genetics, if a male and female each have one dominant and one recessive gene for blue eyes, then there is a 25% chance that their child will have blue eyes. If a random sample of 40 such pairs of expectant parents are studied, what is the likelihood that at least 16 of them will have blue-eyed babies?

(a) What is the mean of the sampling distribution of the sample proportion?

(b) What is the standard deviation of the sampling distribution of the sample proportion? (Round your answer to four decimal places.)

(d) If a random sample of 40 such pairs of expectant parents is studied, what is the likelihood that at least 16 of them will have blue-eyed babies? (Use a table or technology. Round your answer to four decimal places.)

Answer 1

here this is binomial with parameter n=40 and p=0.25

a)

mean p^ =0.25

b)

standard deviation σ=√p(1-p)/n =0.0685

c)

P(X>=16)=1-P(X<=15)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.0262