Reading Binomial Tables

Binomial tables are used to read off probabilities for the Binomial(n, $p$ ) distribution. The standard table then simply gives values from the formula $P(S=s) = (\binom{n}{s}) p^{s} (1 - p)^{(1 - s)}$ for various values of n, $p$ and $s = 0, 1, . . ., n$ . In the current age the computer you are reading this on can also simply calculate these numbers, however often they are useful to know especially if you need to use tables in an exam.

The following table gives a part of the typical tables that can be found in texts or reference books. For the example I have chosen $n = 10$ .

n	s	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
10	0	0.349	0.107	0.028	0.006	0.001	0.000	0.000	0.000	0.000
	1	0.387	0.268	0.121	0.040	0.010	0.002	0.000	0.000	0.000
	2	0.194	0.302	0.233	0.121	0.044	0.011	0.001	0.000	0.000
	3	0.057	0.201	0.267	0.215	0.117	0.042	0.009	0.001	0.000
	4	0.011	0.088	0.200	0.251	0.205	0.111	0.037	0.006	0.000
	5	0.001	0.026	0.103	0.201	0.246	0.201	0.103	0.026	0.001
	6	0.000	0.006	0.037	0.111	0.205	0.251	0.200	0.088	0.011
	7	0.000	0.001	0.009	0.042	0.117	0.215	0.267	0.201	0.057
	8	0.000	0.000	0.001	0.011	0.044	0.121	0.233	0.302	0.194
	9	0.000	0.000	0.000	0.002	0.010	0.040	0.121	0.268	0.387
	10	0.000	0.000	0.000	0.000	0.001	0.006	0.028	0.107	0.349

This table shows a typical block of the Binomial Tables. The first column shows n, the second shows s which ranges from zero to n. Each row following this gives in the column the distribution that accords with values for $p$ across the first row. So the column denoted "0.4" gives the distribution for the Binomial(10,0.4) distribution. To read off a probability, we simply choose the block according to the value of n, the rows of this block according to the value of s, and the column according to $p$ . The number in that cell is then the corresponding probability.

A typical 'student' question is what happens if $p$ is not one of the values across the top row. The answer is that you should use the computer and look it up correctly, the table cannot give every value. Since these tables are mostly used for exam purposes where you are not supposed to have a computer, then professors are forced to make the examples result in one of the available choices. At least that is how it works in my class.

Distributed By Themewagon