A genetics expert has determined that for certain couples, there is a 0.25 probability that any child will have an X-linked recessive disorder.
a. Find the probability that among 200 such children, at least 65 have the X-linked recessive disorder.
b. A subsequent study of 200 actual births reveals that 65 of the children have the X-linked recessive disorder. Based on these sample results, construct a 95% confidence interval for the proportion of all such children having the disorder.
c. Based on parts (a) and (b), does it appear that the expert's determination of a 0.25 probability is correct? Explain.