Labor force participation among women rose in the United States between 1975 and 2000 and has beeen declining ever since. According to the U.S. Bureau of Labor Statistics, 54\% of women were in the labor force in 2015.
If 180 working age women are randomly selected, what is the probability that between $52 \%$ and $61 \%$ are in the labor force? Round your answer to 4 decimal places.
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Step 1 ：This problem is about the binomial distribution. The binomial distribution model is appropriate for a sequence of n trials, or observations, each of which results in a success with probability p and a failure with probability 1-p. In this case, each woman is a trial, being in the labor force is a success, and not being in the labor force is a failure.

Step 2 ：The probability of success, p, is given as 54%, or 0.54.

Step 3 ：We want to find the probability that the number of successes is between 52% and 61% of 180, or between 94 and 110.

Step 4 ：Let's denote the number of trials as n, which is 180 in this case.

Step 5 ：Let's denote the probability of success as p, which is 0.54 in this case.

Step 6 ：Using these values, we can calculate the probability.

Step 7 ：The probability that between 52% and 61% of 180 randomly selected working age women are in the labor force is \(\boxed{0.6875}\).