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A)In the following problem, check that it is appropriate to use the normal approximation to the binomial

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A)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 that 3.8% of the general population will live past their 90th birthday. In a graduating class of 728 high 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
B)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 put 86% of children at risk. A concerted effort was made to remove lead from the environment. Now, suppose only 15% of children in the United States are at risk of high blood-lead levels.
(1) In a random sample of 184 children 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.)
(2) In a random sample of 184 children taken now, what is the probability that 50 or more have high blood-lead levels? (Round your answer to three decimal places.)
C)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 known that 75% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 70 new products, find the following probabilities. (Round your answers to four decimal places.)
(a) within 2 years 47 or more fail
(b) within 2 years 58 or fewer fail
(c) within 2 years 15 or more succeed
(d) within 2 years fewer than 10 succeed
E. Based on long experience, an airline found that about 5% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 264 ticket reservations for an airplane with only 255 seats.
Because the normal approximation to the binomial will be used, the original probability statement P(r ≤ 255)
 must be rewritten using the continuity correction. The continuity correction to the normal approximation is the process of converting the discrete random variable r (number of successes) to the continuous normal random variable x by doing the following.
If r is a left point of an interval, subtract 0.5 to obtain the corresponding normal variable x; that is, x = r − 0.5.
If r is a right point of an interval, add 0.5 to obtain the corresponding normal variable x; that is, x = r + 0.5.
Applying the continuity correction, the desired probability statement P(r ≤ 255)
 becomes P(x ≤....?...)