# Binomial distribution and lottery

1. Feb 20, 2012

### FelixHelix

Hi there, I'm looking at a problem and wanted some help to advise if I'm going in the right direction.

I need to test if the number of times a lotto ball has appeared in a draw fits a binomial distribution. I have collated the data and ultimately will do a hypothesis test.

The draw consists of 5 balls from 1-50. there have been 347 draws to date and therefore 1735 balls drawn. Taking ball number 1 which has been drawn 31 times as an example I need to check that if the number of times it has been drawn fits a binomial distribution.

I know the formula for the bin. dist but wondered what values for the probability and what number I would need to use. Once I know this would I then set up a hypothesis test at 5% siginificance level to see if the null hypothesis is rejected or accepted?

felix

2. Feb 20, 2012

### moonman239

What you'd want to do is perform a two-tailed z-test (since np and n(1-p) are > 5) with mean = 347/50 and sd = sqrt(347/50 * 49/50).

3. Feb 21, 2012

### FelixHelix

When you say two tailed would my X's (r.v) be the lowest value of a number appearing (in this case 25) and the highest (and 51). Add a continuity correction 24.5 and 51.5 respectively and calculate the z test and see if it is significant?