Question

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who 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.
For the company’s sample, the probability that the proportion of people who are in the labor force is greater than 0.65 is ______.

0.6179

0.3000

0.1179

0.3836

Answer 1

Answer:

Option D

Step-by-step explanation:

Given that the BLS reported in February 2012 that the labor force participation rate in the United States was 63.7%

Let P = 63.7% = 0.637

Sample size n=120

Sample proportion p will be normal with mean = 0.637 and

std error = $\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{{0.637(1-0.637)}{120} } \\=0.0439$

required probability

= the probability that the proportion of people who are in the labor force is greater than 0.65

=$P(p>0.65)\\=P(Z>\frac{0.65-0.637}{0.0439} \\=P(Z>+0.296)\\= 0.5-0.1179\\=0.3821$

APproximately option D is right.