Question

According to an​ airline, flights on a certain route are on time 85​% of the time. Suppose 25 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 exactly17 flights are on time.

​(c) Find and interpret the probability that fewer than17 flights are on time.

​(d) Find and interpret the probability that at least 17 flights are on time.

​(e) Find and interpret the probability that between 15 and 17 flights, inclusive, are on time.

​(a) Identify the statements that explain why this is a binomial experiment. Select all that apply.

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

B.The trials are independent.

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

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

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

F.The experiment is performed a fixed number of times.

G.Each trial depends on the previous trial.

​(b) The probability that exactly 17 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 17 flights being on time.

​(Round to the nearest whole number as​ needed.)

​(c) The probability that fewer than 17 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 17 flights being on time.

​(Round to the nearest whole number as​ needed.)

​(d) The probability that at least 17 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 17 flights being on time.

​(Round to the nearest whole number as​ needed.)

​(e) The probability that between 15 and 17 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 15 and 17 flights, inclusive, being on time.

Answer 1

a) statements that explain why this is a binomial experiment-

B.The trials are independent

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

b) P( success) = p= 0.85

n= 25

X be the number of flights on time

X~ Bin( 25, 0.85)

P(X= 17) = ²⁵C₁₇ (0.85)¹⁷ (1-0.85) ⁸ = 0.0175

The probability that exactly 17 flights are on time is 0.0175

In 100 trials of this​ experiment, it is expected about 1.75 to result in exactly 17 flights being on time.

C) P(X< 17) = 0.0079

In 100 trials of this​ experiment, it is expected about 0.79 to result in fewer than 17 flights being on time.

D) P( X>= 17) = 0.9920

The probability that at least 17 flights are on time is time 0.9920

In 100 trials of this​ experiment, it is expected about 99.2 to result in at least 17 flights being on time.

E) P( 15=<X <= 17) = P(X=15) +P(X= 16) + P(X=17) = 0.0249

The probability that between 15 and 17 flights, inclusive, are on time is 0.0249

​

In 100 trials of this​ experiment, it is expected about 2.48 to result in between 15 and 17 flights, inclusive, being on time.