Question

Suppose that 55% of voters will vote “YES” to proposition 30. If we take a sample of size 100, what is the probability that the sample proportion exceeds 50%?

Answer 1

Solution

Given that,

p = 55% =0.55

1 - p = 1- 0.55 =0.45

n = 100

= p = 0.55

=  [p( 1 - p ) / n] = [0.55(0.45) / 100 ] = 0.0497

P( > 0.50 ) = 1 - P( < 0.50)

= 1 - P(( - ) / < (0.50-0.55) /0.0497 )

= 1 - P(z < -1.01)

= 1 - 0.1562

= 0.8438

PROBABILITY = 0.8438