Q:

2. In a given population of two-earner male-female couples, male earnings have a mean of $40,000 per year and a standard deviation of $12,000. Female earnings have a mean of $45,000 per year and a standard deviation of $18,000. The correlation between male and female earnings for a couple is 0.80. Let C denote the combined earnings for a randomly selected couple. What is the mean of C?

Accepted Solution

A:
Answer: $85,000Step-by-step explanation:Given : In a given population of two-earner male-female couples, male earnings have a mean of $40,000 per year and a standard deviation of $12,000. [tex]\mu_M=40,000\ \ ;\sigma_M=12,000[/tex]Female earnings have a mean of $45,000 per year and a standard deviation of $18,000.[tex]\mu_F=45,000\ \ ;\sigma_F=18,000[/tex]If  C denote the combined earnings for a randomly selected couple. Then, the mean of C will be :-[tex]\mu_c=\mu_M+\mu_F\\\\=40,000+45,000=85,000[/tex]Hence, the mean of C = $85,000