Question

 

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 3.5% of the general population will live past their 90th birthday. In a graduating class of 759 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

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.

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

(a) 12 or fewer fish were caught


(b) 5 or more fish were caught


(c) between 5 and 12 fish were caught

Based on long experience, an airline found that about 6% 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 263 ticket reservations for an airplane with only 255 seats.

(a) What is the probability that a person holding a reservation will show up for the flight?


(b) Let n = 263 represent the number of ticket reservations. Let r represent the number of people with reservations who show up for the flight. What expression represents the probability that a seat will be available for everyone who shows 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 and part (b) to answer the following question: What is the probability that a seat will be available for every person who shows up holding a reservation? (Round your answer to four decimal places.)

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

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


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

Answer 1