According to an airline, flights on a certain route are on time 75% of the time. Suppose 10 flights are randomly selected and the number of on-time flights is recorded.
(a) Explain why this is a binomial experiment.
(b) Find and interpret the probability that exactly 6 flights are on time.
(c) Find and interpret the probability that fewer than 6 flights are on time.
(d) Find and interpret the probability that at least 6 flights are on time.
(e) Find and interpret the probability that between 4 and 6 flights, inclusive, are on time.(a) Identify the statements that explain why this is a binomial experiment. Select all that apply.
A. The experiment is performed a fixed number of times.
B. Each trial depends on the previous trial.
C. The experiment is performed until a desired number of successes is reached.
D. There are two mutually exclusive outcomes, success or failure.
E. There are three mutually exclusive possibly outcomes, arriving on-time, arriving early, and arriving late.
F. The probability of success is the same for each trial of the experiment.
G. The trials are independent.(b) The probability that exactly 6 flights are on time is . (Round to four decimal places as needed.)
Interpret the probability.In 100 trials of this experiment, it is expected about to result in exactly 6 flights being on time. (Round to the nearest whole number as needed.)
(c) The probability that fewer than 6 flights are on time is . (Round to four decimal places as needed.)
Interpret the probability.In 100 trials of this experiment, it is expected about to result in fewer than 6 flights being on time. (Round to the nearest whole number as needed.)
(d) The probability that at least 6 flights are on time is . (Round to four decimal places as needed.)
Interpret the probability.In 100 trials of this experiment, it is expected about to result in at least 6 flights being on time. (Round to the nearest whole number as needed.)
(e) The probability that between 4 and 6 flights, inclusive, are on time is . (Round to four decimal places as needed.)
Interpret the probability.In 100 trials of this experiment, it is expected about to result in between 4 and 6 flights, inclusive, being on time. (Round to the nearest whole number as needed.)