When people get married for the first time, the husband is, on average, 2 years older than the wife. The standard deviation of the difference in age is roughly 2.5 years. Suppose it is reasonable to assume that the distribution of the difference in age between the husband and the wife is normal. Twelve recently married couples (all first marriages) are to be selected and the average difference in age is to be calculated.
What is the probability that the average age of the wives in the sample is older than the average age of the husbands?