AS/A2 Stats 1 Stats 3

S2 Topic 1: Binomial and Poisson distributions
Use of Binomial tables
You must be able to use statistical tables when working out Binomial probabilities
Binomial cumulative distribution function Below is part of a table showing tabulated values of P(X £ x), where X has a binomial distribution with index n and parameter p.

Use the options here to practice reading values from the tables. Choose values for n, x and p, and use the tables to find the probability. Then check your answer.

n: 5 6 x: 0 1 2 3 4 p: 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 P(X £ x) =

Summary The Binomial distribution has two parameters, n and p. p is the probability of success n is the number of trials Cumulative probability tables are usually provided in examinations. Typically they cover values of p from 0.05 to 0.50, as above, and these values of n: 5,6,7,8,9,10,12,15,20,25,30,40,50. Probabilities involving other values will need either the formula or approximate methods. To find a particular probability, say P(X=3), you must look up P(X£3) and P(X£2) and subtract A note about graphic calculators A graphic calculator, for example the TI-83 or similar model, can work out Binomial probabilities for you. Suppose that X ~ B(12,0.2): P(X=4) is given by binompdf(12,0.2,4)=.1328755507 P(X £ 4) is given by binomcdf(12,0.2,4)=.9274445005 A list of all the probabilites for the distribution B(12,0.2) is given by binompdf(12,0.2) © MathsNet 2001