Poisson approximation to the binomial

An airline knows that overall 3% of its passengers do not turn up for its flights. The airline decides to adopt a policy of selling more tickets than there are seats on a flight. For an aircraft with 196 seats, the airline sold 200 tickets for a particularly flight.

- find the probability than more than 196 passengers turn up for this flight.

the mean is obviously 0.03 x 100 = 6

Now I figured the way of approaching this is that if more than 196 turn up, that means that 0, 1, 2 or 3 people will not turn up (seats 198, 199, 200 and obviously everyone turning up).

Hence: P(X = 0) + P (X = 1) + P(X = 2) + P(X = 3)

Is this the right way to go about it?

- find the probability that there is at least one empty seat on this flight.

1 - P(X = 0) ?

Reply 1

Adjective

12

That's correct, and in more detail than is necessary - an easier way would be to simply look up P(X < 4) for λ = 6.

Reply 2

Bugzy

OP

10

Adje

That's correct, and in more detail than is necessary - an easier way would be to simply look up P(X < 4) for λ = 6.

Aha - that is true.

Thanks for the clarification.

Reply 3

Bugzy

OP

10

How about this?

20% of letters to be posted are marked first class. One monday morning there are only 12 first class stamps. Given that there are 70 letters to be posted that day:

- use a suitable approximation to find the probability that there are enough first class stamps.

Binomial springs to mind? In which case would it be:

70 C 12 . (0.2)^12 . (0.8)^58 ?

Since we have 12 stamps that are first class; and thus the other 58 will be non-second-class?

Reply 4

Bugzy

OP

10

God needs to put more further mathematicians (or people doing s2) on his planet!

Reply 5

godknows

Original post by Bugzy

How about this?

20% of letters to be posted are marked first class. One monday morning there are only 12 first class stamps. Given that there are 70 letters to be posted that day:

- use a suitable approximation to find the probability that there are enough first class stamps.

Binomial springs to mind? In which case would it be:

70 C 12 . (0.2)^12 . (0.8)^58 ?

Since we have 12 stamps that are first class; and thus the other 58 will be non-second-class?

hey did u manage to figure it out?

Poisson approximation to the binomial

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