a) In the 1999-2000 NHANES report, the reported cancer rate for women subjects age 65 and older is 14%. Using this estimate as the true percentage of all females ages 65 and over who have been told by a health care provider that they have cancer, find the probability that if 250 women are selected at random from the population, more than 18% will have been told they have cancer.

b) In the same report, the cancer rate for men ages 65 and older is 23%. Use this estimate as the percentage of all men ages 65 and older who have been told by a healthcare provider that they have cancer. Find the probability that among 210 men selected at random that fewer than 20% will have been told they have cancer.

c) Find the probability that the male cancer rate is at least 3% higher than the female cancer rate in the two samples given above.