Question

According to an​ airline, flights on a certain route are on time 8080​% of the time. Suppose 1515 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 99 flights are on time. ​(c) Find and interpret the probability that fewer than 99 flights are on time. ​(d) Find and interpret the probability that at least 99 flights are on time. ​(e) Find and interpret the probability that between 77 and 99 ​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 until a desired number of successes is reached. B. The trials are independent. C. The probability of success is the same for each trial of the experiment. D. The experiment is performed a fixed number of times. E. Each trial depends on the previous trial. F. There are two mutually exclusive​ outcomes, success or failure. G. There are three mutually exclusive possibly​ outcomes, arriving​ on-time, arriving​ early, and arriving late. ​(b) The probability that exactly 99 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 99 flights being on time. ​(Round to the nearest whole number as​ needed.) ​(c) The probability that fewer than 99 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 99 flights being on time. ​(Round to the nearest whole number as​ needed.) ​(d) The probability that at least 99 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 99 flights being on time. ​(Round to the nearest whole number as​ needed.) ​(e) The probability that between 77 and 99 ​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 77 and 99 ​flights, inclusive, being on time. ​(Round to the nearest whole number as​ needed.)

Answer 1

Solution:-

​(a)

B) The trials are independent.

C) The probability of success is the same for each trial of the experiment.

D) The experiment is performed a fixed number of times.

F) There are two mutually exclusive​ outcomes, success or failure.

​(b) The probability that exactly 9 flights are on time is 0.043.

x = 9, n = 15

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x = 9) = 0.043

In 100 trials of this​ experiment, it is expected about 4 to result in exactly 9 flights being on time.

(c) The probability that fewer than 9 flights are on time. ​

x = 9, n = 15

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x < 9) = 0.0181

In 100 trials of this​ experiment, it is expected about 2 to result in fewer than 9 flights being on time.

(d) The probability that at least 9 flights are on time is 0.9819.

x = 9, n = 15

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x > 9) = 0.9819

In 100 trials of this​ experiment, it is expected about 98 to result in at least 9 flights being on time.

​(e) The probability that between 7 and 9 ​flights, inclusive, are on time is 0.0569

x₁ = 7, x₂ = 9

By applying binomial distribution

P(x,n) = ⁿC_x*p^x*(1-p)^(n-x)

P(7 < x < 9) = P(x > 7) - P(x > 9)

P(7 < x < 9) = 0.9958 - 0.9389

P(7 < x < 9) = 0.0569

In 100 trials of this​ experiment, it is expected about 6 to result in between 7 and 9 ​flights, inclusive, being on time. ​