Question: The distribution of a test’s scores for college-bound male seniors has a mean of 533 and a standard…

The distribution of a test’s scores for college-bound male seniors has a mean of 533 and a standard deviation of 122. The distribution of a test’s scores for college-bound female seniors has a mean of 518 and a standard deviation of 112. One male and one female are randomly selected. Assume their scores are independent.

Find the mean and standard deviation of the sum of their scores.

What is the mean of the sum of their scores?

(Type an integer or a decimal. Do not round.)

Solution

The problem involves calculating the mean and standard deviation of the sum of scores for one male and one female. Here’s how to solve it: 1. Identify the means and standard deviations: - Mean of male scores (\(\mu_m\)) = 533 - Mean of female scores (\(\mu_f\)) = 518 2. Calculate the mean of the sum of their scores: \[ \mu_{\text{sum}} = \mu_m + \mu_f = 533 + 518 \] 3. Perform the addition: \[ \mu_{\text{sum}} = 1051 \] The mean of the sum of their scores is 1051.