Question

The proportion of eligible voters in the State election who will vote for the incumbent is assumed to be 50%. What is the probability that in a random sample of 400 voters less than 48% say they will vote for the incumbent?

Answer 1

Solution

Given that,

p = 0.50

1 - p = 1-0.50=0.50

n = 400

= p =0.50

=  [p ( 1 - p ) / n] =   [(0.50*0.50) / 400 ] = 0.025

P( < 0.48) =

= P[( - ) / < (0.48-0.50) /0.025 ]

= P(z < -0.8)

Using z table,   

probability =0.2119