In the United States, the generation of people born between 1946 and 1964 are known as baby boomers, and the generation of people born between 1981 and 1996 are known as millennials. Currently, 18 percent of the population are baby boomers and 27 percent of the population are millennials. A random sample of 500 people will be selected. Let the random variable BB represent the number of baby boomers in the sample, and let the random variable MM represent the number of millennials in the sample. By how much will the mean of MM exceed the mean of BB ?

Each person has a probability of 0.18 for being Baby boomer and a probability of 0.27 for being Milennial. We can treat B and M as Binomial distributions, because the probability that a person is milenial or Baby boomer shouldnt change significantly by removing less than 500 elements of the population which is huge in comparison.

Thus, the mean of a binomial distribution is n*p, where n is the amount of tries for the experiment and p is the probability of success in each separate outcome. Here n is 500, thus

The mean of M is 500*0.27 = 135

the mean of B is 500*0.18 = 90

As a result, the mean of M exceeds the mean of B by 135-90 = 45.