Question
In: Statistics and Probability
According to an? airline, flights on a certain route are on time 80?% of the time....
According to an? airline, flights on a certain route are on time 80?% 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 8 flights are on time. ?(c) Find and interpret the probability that fewer than 8 flights are on time. ?(d) Find and interpret the probability that at least 8 flights are on time. ?(e) Find and interpret the probability that between 6 and 8 ?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. The trials are independent. C. The probability of success is the same for each trial of the experiment. D. There are three mutually exclusive possibly? outcomes, arriving? on-time, arriving? early, and arriving late. E. The experiment is performed a fixed number of times. F. Each trial depends on the previous trial. G. The experiment is performed until a desired number of successes is reached. ?(b) The probability that exactly 8 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 8 flights being on time. ?(Round to the nearest whole number as? needed.) ?(c) The probability that fewer than 8 flights are on time is nothing. ?(Round to four decimal places as? needed.)
Solutions
Expert Solution
a) Explain why this is a binomial experiment.
Answer: A. There are two mutually exclusive? outcomes, success or failure.
B. The trials are independent.
C. The probability of success is the same for each trial of the experiment.
E. The experiment is performed a fixed number of times.
?(b) Find and interpret the probability that exactly 8 flights are on time.
Let X be the number of flights are on time
X ~ binomial( 13, 0.80)
The Excel Command is =BINOM.DIST(8,13,0.8,FALSE)
Interpretation: There are 6.91% chances that out of 13, exactly 8 flights are on time
(c) Find and interpret the probability that fewer than 8 flights are on time
The Excel Command is =BINOM.DIST(7,13,0.8,TRUE)
Interpretation : There are only 3% chances that out of 13 , fewer than 8 flights are no time.
?(d) Find and interpret the probability that at least 8 flights are on time
Excel Command : =1-BINOM.DIST(7,13,0.8,TRUE)
Interpretation : there are approximately 97% of chances that out of 13 flights at least 8 flights are on time.
?(e) Find and interpret the probability that between 6 and 8 ?flights, inclusive, are on time.
Interpretation : There are 7.79% chance that out of 13, 6 to 8 ( inclusive) flights are on time.
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