According to an airline, flights on a certain route are on time 75% of the time.

Question

According to an airline, flights on a certain route are on time 75% of the time. Suppose 17 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 10 flights are on time. (c) Find and interpret the probability that fewer than 10 flights are on time. (d) Find and interpret the probability that at least 10 flights are on time. (e) 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 or failure. 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. the probability of success is the same for each trial of the experiment. F. The trials are independent. G. the experiment is performed a fixed number of times.

Explanation / Answer

Ans:a)A.There are two mutually exclusive outcomes,success or failure.

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

F.The trials are independent.

G.The experiment is performed fixed number of times.

b) n=17

Probability of success,p=0.75

Probability of failure,1-p=0.25

P(k=10)=17C10 0.7510 *0.257 ==BINOMDIST(10,17,0.75,FALSE)=0.066845

6.68 % of the time 10 flights reach on time.

b)Probability that fewer than 10 reach on time i.e atmost 9 flights reach on time=P(k<10)=P(k<=9)

=BINOMDIST(9,17,0.75,TRUE)=0.04024

c)Probability tha at least 10 flights are on time=P(k>=10)=1-P(k<=9)=1-0.04024=0.95976

d)Probability that between 8 and 10 flights reach on time i.e. 8 ,9 or 10 flights reach on time =P(8<=k<=10)

=P(k=8)+P(k=9)+P(k=10)

=BINOMDIST(8,17,0.75,FALSE)+BINOMDIST(9,17,0.75,FALSE)+BINOMDIST(10,17,0.75,FALSE) =0.0093+0.0279+0.0668

=0.1040

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.