SOLUTION: The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its fligh
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Question 1152675: The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air had the best rate with 80 % of its flights arriving on time. A test is conducted by randomly selecting 14 Southwest flights and observing whether they arrive on time. Find the probability that at least 12 flights arrive on time. Answer by jim_thompson5910(35256) (Show Source):
Either the flight is on time (success) or it is not on time (failure). Let's assume, for the sake of simplicity, that each flight is independent of any other flight. Based on that, this means we have a binomial problem.
We will use the binomial PDF function
to compute individual binomial probabilities.
The expression represents the binomial coefficient. It can be found alternatively through Pascal's Triangle. The exclamation marks represent factorials.
Plug in n = 14 and p = 0.8 to get
From here we need to compute B(x) for x = 12, 13 and 14.
Then we'll add up those results.
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Plug in x = 12
This represents the approximate probability of exactly 12 flights are on time.
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Plug in x = 13
This represents the approximate probability of exactly 13 flights are on time.
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Plug in x = 14
This represents the approximate probability of exactly 14 flights are on time.
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Add up the results to find the probability that x is 12 or larger.
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