When is n considered large and how close to 0.5 for p? (Approximating a binomial dist

Hi, just going through this on the Edexcel book. I can't find where it says what the actual amount is for n to be considered large. Also, what is considered close to 0.5?

Thanks

Reply 1

shaunjro

Original post

by makin

Hi, just going through this on the Edexcel book. I can't find where it says what the actual amount is for n to be considered large. Also, what is considered close to 0.5?
Thanks

hello! my teacher taught us that n is considered large when n is equal or greater than 50 (i know for some they may have been taught 30) and the range for p for it being close to 0.5 is 0.3<p<0.7

Reply 2

shaunjro

Original post

by shaunjro

hello! my teacher taught us that n is considered large when n is equal or greater than 50 (i know for some they may have been taught 30) and the range for p for it being close to 0.5 is 0.3<p<0.7

although I did get taught this a few weeks ago so my memory isn't the clearest so I may have actually been taught 30 so i'll wait for others to respond too

Reply 3

mqb2766

A simple interpretation of (part of) the above is that you want 0 to be in the left tail of the normal approximation. So you want
mean > 3 std devs
Similarly you want n to be in the right tail of the normal approximation (large p).

Otherwise if 0 lies in the body of the normal approximation, then the left tail will be effectively truncated and actual binomial distribution willl not be approximately symmetric, which is obviously an assumption of the normal approximation. Similarly for n being in the right tail.

So the n=30, p=0.3 corresponds to mean=9, sigma=2.5 and their ratio is 3.6 which is getting close to 3 but ok.
https://homepage.divms.uiowa.edu/~mbognar/applets/bin.html
If you reduced p to 0.1 say, then mean=3, sigma=1.6, and the ratio is about 2. You should be able to see that the distribution is not symmetric and the left tail (normal approximation) would effectively be truncated. Reducing n or p further makes the effect more obvious (and the ratio is << 3).

(edited 1 year ago)

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