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 \(\boxed{0.6875}\).