91Ó°ÊÓ

A married couple plans to have four children, and they are wondering how many boys they should expect to have. Assume none of the children will be twins or other multiple births. Also assume the probability that a child will be a boy is \(0.50 .\) Explain why this is a binomial experiment. Check all four required conditions.

For each situation, identify the sample size \(n\), the probability of a success \(p\), and the number of success \(x .\) When asked for the probability, state the answer in the form \(b(n, p, x)\). There is no need to give the numerical value of the probability. Assume the conditions for a binomial experiment are satisfied. A 2017 Gallup poll found that \(53 \%\) of college students were very confident that their major will lead to a good job. a. If 20 college students are chosen at random, what's the probability that 12 of them were very confident their major would lead to a good job? b. If 20 college students are chosen at random, what's the probability that 10 of them are not confident that their major would lead to a good job?

According to the Centers of Disease Control and Prevention, \(44 \%\) of U.S. households still had landline phone service. Suppose a random sample of 60 U.S. households is taken. a. Find the probability that exactly 25 of the households sampled still have a landline. b. Find the probability that more than 25 households still have a landline. c. Find the probability that at least 25 households still have a landline. d. Find the probability that between 20 and 25 households still have a landline.

The use of drones, aircraft without onboard human pilots, is becoming more prevalent in the United States. According to a 2017 Pew Research Center report, \(59 \%\) of American had seen a drone in action. Suppose 50 Americans are randomly selected. a. What is the probability that at least 25 had seen a drone? b. What is the probability that more than 30 had seen a drone? c. What is the probability that between 30 and 35 had seen a drone? d. What is the probability that more than 30 had not seen a drone?

A 2017 Pew Research Center report on drones found that only \(24 \%\) of Americans felt that drones should be allowed at events, like concerts or rallies. Suppose 100 Americans are randomly selected. a. What is the probability that exactly 25 believe drones should be allowed at these events? b. Find the probability that more than 30 believe drones should be allowed at these events. c. What is the probability that between 20 and 30 believe drones should be allowed at these events? d. Find the probability that at most 70 do not believe drones should be allowed at these events.

According to a study by the Colorado Department of Transportation, \(25 \%\) of Colorado drivers admit to using their cell phones to send texts while driving. Suppose two Colorado drivers are randomly selected. a. If the driver texts while driving, record a \(\mathrm{T}\). If not, record an \(\mathrm{N}\). List all possible sequences of Ts and Ns for the two drivers. b. For each sequence, find the probability that it will occur by assuming independence. c. What is the probability that both drivers text while driving? d. What is the probability that neither driver texts while driving? e. What is the probability that exactly one of the drivers texts while driving?

According to the Pew Research Center, \(53 \%\) of millennials (those born between 1981 and 1997 ) reported using a library or bookmobile within the last year. Suppose that a random sample of 200 millennials is taken. a. Complete this sentence: We would expect of the sample to have used a library or bookmobile within the last year, give or take b. Would it be surprising to find that 190 of the sample have used a library or bookmobile within the last year? Why or why not?