Question

According to an? airline, flights on a certain route are on time 8080?% of the time. Suppose 2525 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 1717 flights are on time. ?(c) Find and interpret the probability that fewer than 1717 flights are on time. ?(d) Find and interpret the probability that at least 1717 flights are on time. ?(e) Find and interpret the probability that between 1515 and 1717 ?flights, inclusive, are on time. ?(a) Identify the statements that explain why this is a binomial experiment. Select all that apply. A. The trials are independent. B. There are three mutually exclusive possibly? outcomes, arriving? on-time, arriving? early, and arriving late. C. Each trial depends on the previous trial. D. The experiment is performed until a desired number of successes is reached. E. There are two mutually exclusive? outcomes, success or failure. F. The experiment is performed a fixed number of times. G. The probability of success is the same for each trial of the experiment. ?(b) The probability that exactly 1717 flights are on time is nothing. ?(Round to four decimal places as? needed.) Interpret the probability. In 100 trials of this? experiment, it is expected about nothing to result in exactly 1717 flights being on time. ?(Round to the nearest whole number as? needed.) ?(c) The probability that fewer than 1717 flights are on time is nothing. ?(Round to four decimal places as? needed.) Interpret the probability. In 100 trials of this? experiment, it is expected about nothing to result in fewer than 1717 flights being on time. ?(Round to the nearest whole number as? needed.)?(d) The probability that at least 1717 flights are on time is nothing. ?(Round to four decimal places as? needed.) Interpret the probability. In 100 trials of this? experiment, it is expected about nothing to result in at least 1717 flights being on time. ?(Round to the nearest whole number as? needed.) ?(e) The probability that between 1515 and 1717 ?flights, inclusive, are on time is nothing. ?(Round to four decimal places as? needed.) Interpret the probability. In 100 trials of this? experiment, it is expected about nothing to result in between 1515 and 1717 ?flights, inclusive, being on time. ?(Round to the nearest whole number as? needed.) Click to select your answer(s).

Answer 1

Given that,

The flights on a certain route are on time 80?% of the time.

That is the probability that the flight is on time is p= 0.80

a) This is an binomial experiment because:

The trials are independent. There are two mutually exclusive? outcomes, success or failure.

The experiment is performed a fixed number of times. G. The probability of success is the same for each trial of the experiment

b) Here n=2525

The probability that exactly 1717 flights are on time is given by

=0

### By using R command;

> dbinom(1717,2525,0.80)
[1] 3.087855e-46

In 100 trials of this? experiment, it is expected about nothing to result in exactly 1717 flights being on time

c)The probability that fewer than 1717 flights are on time is given by

=0

## By using R command:

> pbinom(1716,2525,0.80)
[1] 3.475295e-46

d)  The probability that at least 1717 flights are on time is given by

  

### By using R command

> 1-pbinom(1716,2525,0.80)
[1] 1

In 100 trials of this? experiment, it is expected about 100 to result in at least 1717 flights being on time.

e) The probability that between 1515 and 1717 ?flights, inclusive, are on time is given by:

=0

### By using R command:

> pbinom(1717,2525,0.80)-pbinom(1515,2525,0.80)
[1] 6.56315e-46

In 100 trials of this? experiment, it is expected about nothing to result in between 1515 and 1717 ?flights, inclusive, being on time