Question

Suppose 47% of the population has a retirement account.

If a random sample of size 847 is selected, what is the probability that the proportion of persons with a retirement account will be greater than 52%? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 0.47

1 - p = 1 - 0.47=0.53

n = 8447

= p =0.47

=  [p( 1 - p ) / n] = [(0.47*0.53) /847 ] = 0.0171

P( > 0.52) = 1 - P( <0.52 )

= 1 - P(( - ) / < (0.52 - 0.47) /0.0171 )

= 1 - P(z < 2.92)

Using z table

= 1 -0.9982

=0.0018