Question

Suppose that 55 percent of the voters in a particular region support a candidate. Find the probability that a sample of 900 voters would yield a sample proportion in favor of the candidate within 2 percentage points of the actual proportion.

Answer 1

Solution:

Given that,

n = 900

= 55% =0.55

1 - = 1 - 0.55 = 0.45

=   = 0.55

= ( 1 - ) / n

=   0.55 * 0.45 / 900

= 0.0166

= 0.0166

within 0.02 = 0.55 ± 0.02 = 0.53, 0.57

P( 0.53 < < 0.57 )  

P( 0.53 - 0.55 / 0.0166 ) < ( -    / ) < ( 0.57 - 0.55 / 0.0166 )

P ( - 0.02 /0.0166 < z < 0.02 / 0.0166 )

P ( - 1.20 < z < 1.20 )

P ( z < 1.20 ) - p ( z < -1.20 )

Using z table

= 0.8849 - 0.1151

= 0.7698

Probability = 0.7698