Question

Approximate the binomial probability using the normal distribution. What is the probability that more than 100 out of 300 elections will contain voter fraud? One report suggests that there is a 32% chance of an individual election containing voter fraud.

Answer 1

Solution :

Given that,

p = 0.32

q = 1 - p =1-0.32=0.68

n = 300

Using binomial distribution,

= n * p = 300*0.32=96

= n * p * q = 300*0.32*0.68=8.0796

Using continuity correction

,P(x > 100) = 1 - P(x <100.5 )

= 1 - P((x - ) / < (100.5-96) / 8.0796)

= 1 - P(z <0.56 )   

Using z table   

= 1-0.7123

=0.2877

probability= 0.2877