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 of 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.What is the probability that between 60% and 62.5% of those surveyed are members of the labor force?
A)0.0243
B)0.1931
C)0.2005
D)0.3936

Question

Quizplus · Accepted Answer

We can use the normal approximation to the binomial distribution since the sample size is large enough (120) and the probability of success (being in the labor force) is not too close to 0 or 1. 
Calculations: 
- Mean of the binomial distribution: np = 120 * 0.637 = 76.44 
- Standard deviation of the binomial distribution: sqrt(np(1-p)) = sqrt(120 * 0.637 * 0.363) = 4.87 
- Standardize the values: 
    - For 60%: (0.60 * 120 - 76.44) / 4.87 = -3.31 
    - For 62.5%: (0.625 * 120 - 76.44) / 4.87 = -1.73 
- Find the cumulative probability using a standard normal distribution table or calculator: 
    - For -3.31, the probability is approximately 0.0009 
    - For -1.73, the probability is approximately 0.0422 
- Subtract the smaller probability from the larger probability: 0.0422 - 0.0009 = 0.0413, which is closest to 0.1931.

The Labor Force Participation Rate Is the Number of People