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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?

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Answer: $85,000

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.


\mu_M=40,000\ \ ;\sigma_M=12,000

Female earnings have a mean of $45,000 per year and a standard deviation of $18,000.


\mu_F=45,000\ \ ;\sigma_F=18,000

If C denote the combined earnings for a randomly selected couple.

Then, the mean of C will be :-


\mu_c=\mu_M+\mu_F\\\\=40,000+45,000=85,000

Hence, the mean of C = $85,000

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