Question

According to an​ airline, flights on a certain route are on time 80​% 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. (options provided below)​

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

B.The probability of success is different for each trial of the experiment.

C.Each trial depends on the previous trial.

D.There are three mutually exclusive possibly​ outcomes, arriving​ on-time, arriving​ early, and arriving late.

E.The exeriment is performed a fixed number of times.

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

G.The trials are independent.

H.The experiment is performed until a desired number of successes is reached.

(b) Determine the values of n and p. ​

(c) Find and interpret the probability that exactly 6 flights are on time. ​

(d) Find and interpret the probability that fewer than 6 flights are on time. ​

(e) Find and interpret the probability that at least 6 flights are on time.

​(f) Find and interpret the probability that between 4 and 6 ​flights, inclusive, are on time.

Answer 1

a) The number of on time flights out of the 10 flights here could be modelled as:

This is a binomial experiment as each trial here is independent of each of the other event and the probability of success for each trial ( that is on time flight) on each trial is equal to 0.8

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

G.The trials are independent.

Are the correct options here.

b) The value of n and p are obtained here as:
n = Number of flights that is 10 here.
p = probability of on time flight for each flight = 0.8

Therefore 10 and 0.8 are the required parameters values here.

c) Probability that exactly 6 flights are on time is computed here as:

Therefore 0.0881 is the required probability here.

d) The probability that fewer than 6 flights are on time is computed here as:

Therefore 0.0328 is the required probability here.

e) The probability that at least 6 flights are on time is computed here as:

Therefore 0.9672 is the required probability here.

f) The probability here is computed as:

Therefore 0.1200 is the required probability here.