SOLUTION: The independent probability of a passenger arriving for a booked flight on a Maxi service is 0.8. The airline booked 225 passengers and there are 195 seats available on Maxi..Use t
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Question 614980: The independent probability of a passenger arriving for a booked flight on a Maxi service is 0.8. The airline booked 225 passengers and there are 195 seats available on Maxi..Use the Normal distribution to find the probability for a given flight more booked passengers arrive than there are seats available. Found 2 solutions by stanbon, Theo:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The independent probability of a passenger arriving for a booked flight on a Maxi service is 0.8. The airline booked 225 passengers and there are 195 seats available on Maxi..Use the Normal distribution to find the probability for a given flight more booked passengers arrive than there are seats available.
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Binomial Problem: P(196<= x <=225) with mean = np = 0.8*225 = 180
and std = sqrt(npq) = sqrt(180*0.2) = 6
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normal approximation: P(195.5<= x <=225.5) with u = 180 and s = 6
Ans: normalcdf(195,5,225.5,180,6) = 0.0049
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I used a TI-84 to get that numerical answer.
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Cheers,
Stan H.
You can put this solution on YOUR website! to the best of my knowledge, you are dealing with a binomial distribution that can be approximated by the normal distribution.
see the following reference to see where i'm coming from. http://www.talkstats.com/showthread.php/724-The-Normal-Approximation-to-the-Binomial-Distribution
n = 225 = number of tickets sold.
p = .8 that the person who bought the ticket will actually show up.
mean of the binomial distribution = n*p = 228 * .8 = 180
standard deviation of the binomial distribution = sqrt(n*p*q) = sqrt(225*.8*.2) = sqrt(36) = 6.
so the data you will work with is:
mean = 180
standard deviation = 6
normal distribution.
you want to know the probability that the number of passengers who actually show up is greater than 195 (the capacity of the plane).
the easiest way to find that is to use the z-score calculator by david m. lane in the following link. http://davidmlane.com/normal.html
click on area from a volume
enter mean of 180
enter standard deviation of 6
select above and enter 195
your answer should be equal to .0062
this means that the probability of more than 195 passengers showing up is equal to .0062.
if you need to use the z-score tables, you would calculate the z-score as follows:
z-score = (actual - mean) / standard deviation
this becomes:
z-score = (195 - 180) / 6 which is equal to 2.5
use the same calculator and enter a mean of 0 and a standard deviation of 1 and enter a value above of 2.5 and you should get the same answer.
this is a great tool that takes the burden of finding the z-score in a table and then determining the area to the right of the z-score.
if you need to know how to do that, then look at the following link. http://www.algebra.com/algebra/homework/Probability-and-statistics/change-this-name28108.lesson
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