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. What is the probability that between 60% and 62.5% of those surveyed are members of the labor force

Answer 1

Given : n = 120, p = 0.637 or 63.7%

Here , p is normal, we need to standardize it.

Thus, standard value is given by formula:

Z =

P( 60%< p< 62.5%) = P( p< 62.5) - P(p < 60%)

Using normal approximation,

P( p < pbar) =

P( 0.6< p < 0.625) = -

=   -

= -

= -

= 0.3936 - 0.2005

= 0.1931

Thus, there is 0.1931 Probability that between 60% and 62.5% are from labour force.

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