Question

example 4.9 which of the following are binomial experiments? a) a player rolls a pair of fair dice 10 times. the number x of 7s rolled is recorded. b) the 11 largest airlines had an on - time percentage of 84.7% in november, 2001 according to the air travel consumer report. in order to assess reasons for delays, an official with the faa randomly selects flights until she finds 10 that were not on time. the number of flights x that need to be selected is recorded. c) in a class of 40 students, 50% are female. the instructor randomly selects 4 students. the number x of females selected is recorded.

Explanation:

Step1: Recall binomial experiment criteria

A binomial experiment has a fixed number of trials, each trial is independent, there are only two possible outcomes, and the probability of success is constant for each trial.

Step2: Analyze part a

A player rolls a pair of fair dice 10 times. Each roll is independent. There are two - outcome - related aspects (e.g., getting a 7 or not getting a 7). The probability of getting a 7 on a roll of two dice is constant ($\frac{6}{36}=\frac{1}{6}$). The number of trials $n = 10$ is fixed. So, it is a binomial experiment.

Step3: Analyze part b

The number of trials is not fixed in advance. We stop when we find 10 non - on - time flights. In a binomial experiment, the number of trials $n$ must be fixed. So, it is not a binomial experiment.

Step4: Analyze part c

The instructor randomly selects 4 students from 40 students. Each selection is not independent (because when one student is selected, the probability for the next selection changes). In a binomial experiment, trials must be independent. So, it is not a binomial experiment.

Answer:

a) is a binomial experiment; b) is not a binomial experiment; c) is not a binomial experiment.