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

It is estimated that 3.5% of the general population will live pasttheir 90th birthday. In a graduating class of 759 high schoolseniors, find the following probabilities. (Round your answers tofour 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

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

Ocean fishing for billfish is very popular in the Cozumel region ofMexico. In the Cozumel region about 47% of strikes (while trolling)resulted in a catch. Suppose that on a given day a fleet of fishingboats got a total of 27 strikes. Find the following probabilities.(Round your answers to four decimal places.)

ASK YOUR TEACHER

Based on long experience, an airline found that about 6% of thepeople making reservations on a flight from Miami to Denver do notshow up for the flight. Suppose the airline overbooks this flightby selling 263 ticket reservations for an airplane with only 255seats.(a) What is the probability that a person holding areservation will show up for the flight?


(b) Let n = 263 represent the number of ticketreservations. Let r represent the number of people withreservations who show up for the flight. What expression representsthe probability that a seat will be available for everyone whoshows up holding a reservation?

P(r ≥ 263)P(r ≤263)    P(r ≥255)P(r ≤ 255

(c) Use the normal approximation to the binomial distribution andpart (b) to answer the following question: What is the probabilitythat a seat will be available for every person who shows up holdinga reservation? (Round your answer to four decimalplaces.)

One environmental group did a study of recycling habits in aCalifornia community. It found that 74% of the aluminum cans soldin the area were recycled. (Use the normal approximation. Roundyour answers to four decimal places.)

(a) If 384 cans are sold today, what is the probability that 300or more will be recycled?


(b) Of the 384 cans sold, what is the probability that between 260and 300 will be recycled?