Question

33. Exhibit 7-8.

The labor force participation rate is the number of people in the labor force divided by the number of people in the country that are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force.

Refer to Exhibit 7-8. For the company's sample, the probability that the proportion of people who are in the labor force is greater than 0.65 is ___________. 
 
 A. 0.3000 B. 0.6179 C. 0.3821 D. 0.1179

NOTE: Correct answer is C. Please legibly walk me through this problem.

Answer 1

Solution

Given that,

p = 63.7% = 0.637

1 - p = 1 - 0.637 = 0.363

n = 120

= p = 0.637

=  [p( 1 - p ) / n] = [0.637*(0.363) /120 ] = 0.0439

P( > 0.65 ) = 1 - P( < 0.65)

= 1 - P(( - ) / < (0.65-0.637) / 0.0439)

= 1 - P(z <0.30)

= 1 - 0.6179= 0.3821

PROBABILITY = 0.3821

C. 0.3821 IS CORRECT