Question

Suppose 56% of the registered voters in a country are Republican.

If a sample of 447 voters is selected, what is the probability that the sample proportion of Republicans will be greater than 60%? Round your answer to four decimal places.

Answer 1

Solution:

Given that,

n = 447

= 0.56

1 - = 1 - 0.56 = 0.44

So,

a ) =   = 0.56

=   ( 1 - ) / n

=   0.56 * 0.44 / 447

= 0.0235

=0.0235

p (   > 0.60 )

= 1 -  p (   < 0.60 )

= 1 - p ( -    / ) < ( 0.60 - 0.56 / 0.0235 )

= 1 - p ( z < 0.04 /0.0235 )

= 1 - p ( z < 1.70 )

Using z table

= 1 - 0.9554

= 0.0446

Probability = 0.0446