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 _______.
A) 0.1179
B) 0.3000
C) 0.3821
D) 0.6179

Question

Quizplus · Accepted Answer

We know that the labor force participation rate in the United States was 63.7%. However, we do not know the proportion of people in the labor force in the company's sample. We can use the normal approximation to the binomial distribution to estimate the probability that the proportion of people who are in the labor force is greater than 0.65.

We can calculate the mean and standard deviation of the sample proportion as follows:

mean = np = 120 * 0.637 = 76.44
standard deviation = sqrt(np(1-p)) = sqrt(120 * 0.637 * (1-0.637)) = 4.72

Then, we can standardize the sample proportion:

z = (0.65 - 0.637) / 0.0472 = 0.275

Using a standard normal table, we can find that the probability of z being greater than 0.275 is approximately 0.3821. Therefore, the probability that the proportion of people who are in the labor force is greater than 0.65 is 0.3821.

The Labor Force Participation Rate Is the Number of People