SOLUTION: From experience, an airline knows that only 73 percent of the passengers booked on a flight from New York to Los Angeles actually board their flight. If this percentage is correct,
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Question 1168965: From experience, an airline knows that only 73 percent of the passengers booked on a flight from New York to Los Angeles actually board their flight. If this percentage is correct, what is the probability that, in a random sample of 6 booked passengers from New York to Los Angeles, exactly 3 show up?
Round your answer to three decimal places. Answer by math_tutor2020(3817) (Show Source):
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p = probability of success
p = probability someone showing up (ie actually boarding their flight)
p = 0.73
n = sample size
n = 6
x = number of people who show up (out of n = 6 people)
x = 3
We'll use the binomial probability distribution formula below
B(x) = (n C x)*(p^x)*(1-p)^(n-x)
B(3) = (6 C 3)*(0.73^3)*(1-0.73)^(6-3)
B(3) = 20*(0.73^3)*(0.27^3)
B(3) = 20*(0.73^3)*(0.27^3)
B(3) = 20*0.389017*0.019683
B(3) = 20*0.007657021611
B(3) = 0.15314043222
B(3) = 0.153
In a sample of 6 people, there's roughly a 15.3% chance of exactly 3 showing up and actually boarding their flight.
Note: The notation 6 C 3 refers to the nCr combination notation. You'll use the formula or you can use Pascals Triangle.
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