In a population of dual-earner male-female couples, the average male income is $40,000 per year with a standard deviation of $12,000, while the average female income is $45,000 per year with a standard deviation of $18,000. The correlation coefficient between male and female incomes within a couple is 0.80. Let C represent the combined income for a randomly chosen couple. What is the average of C?

To find the average combined income (C) for a randomly chosen couple, we simply need to add the average incomes for the males and females.

Given: - The average male income = $40,000 - The average female income = $45,000

The average combined income (C) for a couple is: Average of C = Average male income + Average female income Average of C = $40,000 + $45,000 Average of C = $85,000

So, the average combined income for a randomly chosen couple is $85,000 per year.

Extra: The average, also known as the mean, is a measure of the central tendency. It is derived by adding up all the values of a set of numbers and then dividing the sum by the count of the values. In more complex scenarios where one needs to consider the relationship between two sets of numbers, such as incomes where there could be some level of dependence between a male's income and a female's income (perhaps due to educational or social factors affecting both partners in a similar way), other statistics, such as the covariance or the correlation coefficient, come into play.

However, the question you've asked is asking for the straightforward calculation of the combined average income, which does not require us to use the correlation coefficient. The correlation coefficient, which in this case is given as 0.80, is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of 0.80 suggests a strong positive relationship between male and female incomes within the population studied. This means that if we were to examine differences or variations in income (not the average), we'd expect that if a man has an income higher than the average male income, his partner is also more likely to have an income higher than the average female income, and vice versa. However, this correlation coefficient isn't needed for calculating the average of combined incomes, which is a straightforward addition of the two means.