Using the Binomial distribution

Question

Using the Binomial distribution,

If n=6 and p=0.5, find P(x=6). (round to 4 decimal places)

Answer 1

n=6. p=q= 1/2

find P(x=6) = ?? = P(5.5<x<6.5)

mean = np = 3

var = npq = 1.5

sd = sqrVar = sqr1.5 = about 1.22

z score for x=6.5 is (6.5-3)/1.22 = 3.5/1.22 = about 2.86

z score for x =5.5 is (5.5-3)/1.22 = 2.5/1.22 = about 2.04

use z tables to find the area under the curve for z scores

then subtract to get P(x=6) = 33%