Delta airline flights seats 340 people. An average of 5% of the people with reservations doesnt show up, so they overbook by 350. This system can be analyzed by using binomial distribution. n=350 and p=0.95
1) Find the probablity that 350 reservations there are more passangers then seats. Find P(at least 341 people with reservations show up)
how do I do this????
The mean of the distribution of the number of passengers showing up is n*p and the standard deviation is sqrt [n*p*(1-p)]. Calculate those numbers.
Using these values and the normal distribution tool at
(Broken Link Removed) I get the probability of 341 or more booked passengers showing up to be 1.9%
Might be subtraction.so I don't know this.
To find the probability that there are more passengers than seats, we can use the binomial distribution formula.
The formula for the binomial distribution is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
Where:
- P(X = k) is the probability of having exactly k successes (in this case, passengers showing up)
- n is the number of trials (350 in this case)
- p is the probability of success (passenger showing up, which is 0.95 in this case)
- C(n, k) is the combination formula: C(n, k) = n! / (k! * (n - k)!)
To find the probability that at least 341 people with reservations show up (more passengers than seats), we need to calculate the sum of probabilities for all possible cases from 341 to 350.
P(at least 341 people with reservations show up) = P(X = 341) + P(X = 342) + ... + P(X = 350)
Let's calculate this probability step by step:
First, calculate the probability for each case:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
For k = 341:
P(X = 341) = C(350, 341) * 0.95^341 * (1 - 0.95)^(350 - 341)
Repeat this calculation for k = 342 to k = 350.
Finally, calculate the sum of all these probabilities:
P(at least 341 people with reservations show up) = P(X = 341) + P(X = 342) + ... + P(X = 350)
Using this approach, you can find the probability that there are more passengers than seats for Delta airline flights.