Statistics Probability: Please show work on all questions:

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.

More than a decade ago, high levels of lead in the blood put87%of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only9%of children in the United States are at risk of high blood-lead levels.

(a) In a random sample of204children taken more than a decade ago, what is the probability that 50 or more had high blood-lead levels? (Round your answer to three decimal places.)

(b) In a random sample of204children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)

****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.

It is estimated that3.4%of the general population will live past their 90th birthday. In a graduating class of730high school seniors, find the following probabilities. (Round your answers to four decimal places.)

(a) 15 or more will live beyond their 90th birthday

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

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

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