1.In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.According to the American Red Cross, type O-positive blood is the most common blood type in America, and as a result it is in very high demand. Approximately 38% of all Americans have blood type O-positive. Suppose the 61 blood donors at a given clinic represent a random sample of Americans. (Round your answers to four decimal places.)

(a)What is the probability that at least 25 have blood type O-positive?

(b)What is the probability that at most 20 have blood type O-positive?

(c)What is the probability that fewer than 30 do not have blood type O-positive?

(d)What is the probability that more than 35 do not have blood type O-positive?

2.In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.Suppose it is estimated that3.7% of the general population will live past their 90th birthday. In a graduating class of769high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a)30 or more will live beyond their 90th birthday

(b)between 25 and 35 will live beyond their 90th birthday

(c)more than 40 will live beyond their 90th birthday

3.In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities.

Suppose more than a decade ago, high levels of lead in the blood put 87% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 8% of children in the United States are at risk of high blood-lead levels.

(a)In a random sample of 212 children taken more than a decade ago, what is the probability that 50 or more had high blood-lead levels? (Round your answer to four decimal places.)

(b)In a random sample of 212 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to four decimal places.)