Here's the problem
Ok. I've typed the problem out and answered it to the best I can.
Please help. Any feedback at all will help!
There's a plane with 213 seats. Because some people with reservations don’t show up, the company overbooks the plane by accepting more passenger reservations than seats, in order to increase revenue.
It is assumed there is a probability of 0.0995 that a passenger with a reservation will not show up for the flight.
It is also assumed that the airline booked 236 reservations for the 213 seated airplane.
Find the probability that when 236 reservations are accepted, more passengers show up than the amount of seats available. In other words, find the probability of more than 213 people showing up with reservations, when 236 reservations were accepted.
n = 236 - # of reservations made for the plane
r = 213 - # of plane seats available
p = .0995 – probability that a passenger wit ha reservation will NOT show up
q = .9005 - probability that a passenger with a reservation will show up.
P(more than 213 passengers show up)
Since the probability deals with “more than, >” and not an exact value, solving the probability requires a cut off mark and cumulative adding. This accumulated sum must then be subtracted by 1. Thus, I will use
binomcdf (n, q, r)
P (more than 213 passengers show up) = 1 – binomcdf (236, .9005, 213)
1 - binomcdf (236, .9005, 213)
1 - .5735581699 = .4264418301 ≈ .4264
IS this right? Did I use the right probability? Does it make sense? It doesn't seem tight at all to me.
Is the probability of overbooking small enough so that it doesn’t happen very often, or does it seem too high so that changes must be made to make it lower?
It seems fine, because we assume that anything lower than .05 is unusual. .4264 > .05, not less than. So, the probability is not too small.
Using trial and error, find the maximum number of reservations that could be accepted so that the probability of having more passengers than seats is 0.05or less.
This is why my answer didn't make sense for the probability question.
In order to do this, do I use 1-binomcdf or just binomcdf? I'm really confused. Do I do 1-binomcdf(237...240...245..... or just do binomcdf(237...240...245) to manipulate it to be more than .05.