The amount of money that Maria earns in a week is a random variable with a mean of $970 and a standard deviation of $25.The amount of money that Elena earns in a week is a random variable with a mean of $860 and a standard deviation of $10.How much more do you expect Maria to earn in a week than Elena? What is the standard deviation of this difference? Assume that Maria's earnings are independent of Elena's earnings.
A)$1830,$35
B)$110,$26.93
C)$110,$22.91
D)$110,$15
E)$1830,$26.93

Question

Quizplus · Accepted Answer

The difference in earnings, $D$, is given by:

$$D = 	ext{Maria's earnings } - 	ext{ Elena's earnings}$$

The mean of $D$ is:

$$E(D) = E(	ext{Maria's earnings}) - E(	ext{ Elena's earnings}) = \$970 - \$860 = \$110$$

The standard deviation of $D$ is:

$$	ext{Var}(D) = 	ext{Var}(	ext{Maria's earnings}) + 	ext{Var}(	ext{ Elena's earnings}) = 25^2 + 10^2 = 675$$

So, the standard deviation of $D$ is:

$$	ext{SD}(D) = \sqrt{	ext{Var}(D)} \approx \$26.93$$

Therefore, we can expect Maria to earn about \$110 more than Elena, with a standard deviation of \$26.93.

The Amount of Money That Maria Earns in a Week