Question

Poisson Normal Approximation
Suppose that X has a Poisson distribution with a mean of 64. Approximate the following probabilities:

P(X<64) so,

P(X<64) = P( Z < 64-64/(64)^(1/2)) = P(Z < 0) = 0.5

The text book says the answer is 0.4761 what am I doing wrong??

Answer 1

It seems like every answer I get is slightly off from what the textbook answer is.

Answer 2

Sir/Ma'am please show your Working for the question you have posted.

Answer 3

I did

Answer 4

P(X<64) = P( Z < 64-64/(64)^(1/2)) = P(Z < 0) = 0.5

Answer 5

there it is again

Answer 6

are we trying to approximate it with a binomial?

Answer 7

no this is a Poisson distribution approximation

Answer 8

oops sorry for poorly worded question

Answer 9

http://www.stattler.com/article/poisson-approximation-binomial-probabilities

im reading this for a refresher

Answer 10

that is the table im using to get my approximations of the normal distribution, not that it is needed for the question because P(Z<0) = 0.5

Answer 11

The textbook is saying, P(X<64) = P(Z<-0.06)

Answer 12

All my answer are like a few decimals off every time.

Answer 13

it may be that your using a normal distribution instead of a binomial distribution ... but thats just a thought at the moment

Answer 14

are you wanting to approx it with a binomial?

Answer 15

No this question is a poisson distribution approximation using the normal distribution

Answer 16

nothing to do with binomials, I edited my question to avoid confusion sorry again about that

Answer 17

use a continuity correction

Answer 18

oh yeah but why? Isn't it greater than?

Answer 19

there is no equality so why do I have to correct?

Answer 20

you are going from a discrete distribution to a continuous one

Answer 21

So you always have to correct?

Answer 22

you should

Answer 23

Ok thank you so much, sorry for the bother, I should have tried correcting before asking this question ugh

Answer 24

@Zarkon it says right in the textbook,

To correct P(X<x) = P(Z<x+0.5)
To Correct P(X>x) = P(Z>x - 0.5)

For this problem,

P(X<64), therefore,

P(X<64) = P(X<64+0.5) = P(Z<0.063) = 0.532922

SO the text book is in fact wrong.

Answer 25

I'm pretty frustrated atm ugh

Answer 26

\[P(X<64) =P(X\le 63)=P(X\le 63+.5)=P(X\le63.5)=P(Z\le -.0625)\]

Answer 27

Ok I think I finally get this stuff

Answer 28

good