Question

according to flightstats.com, american airlines flights from dallas to chicago are on time 80% of the time. suppose 15 flights are randomly selected, and the number of on - time flights is recorded.
(a) explain why this is a binomial experiment.
(b) determine the values of n and p.
(c) find and interpret the probability that exactly 10 flights are on time.
(d) find and interpret the probability that fewer than 10 flights are on time.
(e) find and interpret the probability that at least 10 flights are on time.
(f) find and interpret the probability that between 8 and 10 flights, inclusive, are on time.
(a) identify the statements that explain why this is a binomial experiment. select all that apply.
□ a. there are two mutually exclusive outcomes, success (plane arrives on time) or failure (plane does not arrive on time).
□ b. the experiment is performed a fixed number of times.
□ c. there are three mutually exclusive possible outcomes, arriving on - time, arriving early, and arriving late.
□ d. the probability of success is the same for each trial of the experiment.
□ e. each trial depends on the previous trial.
□ f. the probability of success is different for each trial of the experiment.

Explanation:

• Option A: A binomial experiment has two mutually - exclusive outcomes. Here, success (on - time) and failure (not on - time) fit this criterion.
• Option B: The experiment is performed \(n = 15\) times (fixed number of trials).
• Option C: A binomial experiment has only two outcomes. Since this option mentions three outcomes, it is incorrect.
• Option D: The probability of success \(p=0.8\) (on - time) is the same for each flight (trial).
• Option E: In a binomial experiment, trials are independent. So, this option is incorrect.
• Option F: In a binomial experiment, the probability of success is constant. So, this option is incorrect.

Answer:

A. There are two mutually exclusive outcomes, success (plane arrives on time) or failure (plane does not arrive on time).
B. The experiment is performed a fixed number of times.
D. The probability of success is the same for each trial of the experiment.