Question

According to flightstats.com, American Airlines flights from Dallas to Chicago are on time 80% of the time. Suppose 25 flights are randomly selected, and the number of on-time flights is recorded.

(a) Explain why this is a binomial experiment. Identify the statements that explain why this is a binomial experiment. Select all that apply.
A. The probability of success is the same for each trial of the experiment.
B. There are two mutually exclusive outcomes, success or failure.
C. The experiment is performed until a desired number of successes are reached.
D. There are three mutually exclusive possible outcomes, arriving on-time, arriving early, and arriving late.
E. The probability of success is different for each trial of the experiment.
F. The trials are independent.
G. Each trial depends on the previous trial.
H. The experiment is performed a fixed number of times.

(b) Using the binomial distribution, determine the values of n and p.
n = (Type an integer or a decimal. Do not round.)

Answer 1

A binomial experiment satisfies the conditions of a fixed number of trials, two possible outcomes for each trial, and independence of the trials. In this case, recording the number of on-time flights out of 25 randomly selected flights is a binomial experiment with n = 25 and p = 0.8.

Step-by-step explanation:

A binomial experiment satisfies the following conditions:

1. There are a fixed number of trials, denoted as n.
2. There are only two possible outcomes, success and failure, for each trial.
3. The trials are independent and repeated under identical conditions.

In this case, the number of on-time flights out of 25 randomly selected flights is being recorded. This fits the criteria for a binomial experiment because the number of trials is fixed at 25, there are two possible outcomes (on-time or not on-time), and each flight is independent of the others.

The probability of success (an on-time flight) is 0.8, as given by the information from flightstats.com. Therefore, the values of n and p for the binomial distribution are n = 25 and p = 0.8.