The labor force participation rate is the number of people i

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%. 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.

What is the probability that less than 60% of those surveyed are members of the labor force?

Solution

So the probability is

P(phat<0.6) = P((phat-p)/sqrt(p*(1-p)/n) <(0.6-0.637)/sqrt(0.637*(1-0.637)/120))

=P(Z<-0.84)

=0.2005 (from standard normal table)

Answer: 0.2005