According to an airline. flights on a certain route are on time 85% of the time.

Question

According to an airline. flights on a certain route are on time 85% of the time. Suppose 13 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 9 flights are on time (c) Find and interpret the probability that fewer than 9 flights are on time (d) Find and interpret the probability that at least 9 flights are on time (e) Find and interpret the probability that between 7 and 9 flights, inclusive, are on time (a) Identify the statements that explain why this is a binomial experiment. Select all that apply A. The probability of success is the same for each trial of the experiment. B. There are two mutually exclusive outcomes, success or failure C. There are three mutually exclusive possibly outcomes, arriving on-time, arriving early, and arriving late D. The experiment is performed until a desired number of successes is reached E. Each trial depends on the previous trial F. The trials are independent. G. The experiment is performed a fixed number of times (b) The probability that exactly 9 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 9 flights being on time (Round to the nearest whole number as needed.) (c) The probability that fewer than 9 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 9 flights being on time (Round to the nearest whole number as needed.) (d) The probability that at least 9 flights are on time is (Round to four decimal places as needed.)

Explanation / Answer

a)

A process to be binomial,

1) You must have fixed number of trials.

2)Each trial is independent event

3)There are only two outcomes.

Therefore, statement B,G and F explains this is binomial experiment.

b)

p(x) = nCx px (1-p)n-x

p(x=9) =  13C9 0.859 0.154

= 0.0838

In 100 trials of this experiment, it is expected about 8 to result in exactly 9 flights being on time.

c)

p(x < 9) = 1 - p (x >=9)

= 1 - [p(x = 9) + p(x=10) + p(x=11) + p(x=12) + p(x=13)]

= 1 - [ 13C9 0.859 0.154 +  13C10 0.8510 0.153 +  13C11 0.8511 0.152 +  13C12 0.8512 0.15 +  13C13 0.8513 0.150 ]

= 0.0342

In 100 trials of this experiment, it is expected about 3 to result in fewer 9 flights being on time.

d)

p(x>=9) =  p(x = 9) + p(x=10) + p(x=11) + p(x=12) + p(x=13)

=  13C9 0.859 0.154 +  13C10 0.8510 0.153 +  13C11 0.8511 0.152 +  13C12 0.8512 0.15 +  13C13 0.8513 0.150

= 0.9658

In 100 trials of this experiment, it is expected about 97 to result in at least 9 flights being on time.

e)

p(7<=x<=9) = p(x <=9) - p(x<=6)

= [1- p(x>10)] - [p(x=6) +p(x=5)+p(x=4)+p(x=3)+p(x=2)+p(x=1)+p(x=0)]

= 0.1180 - 0.0013

= 0.1167

In 100 trials of this experiment, it is expected about 12 to result in between 7 and 9 flights inclusive being on time.

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