Question

Suppose the mean SAT verbal score is 525 with a standard deviation of 100, while the mean SAT math score is 575 with a standard deviation of 100. What can be said about the mean and standard deviation of the combined math and verbal scores

Answer 1

The mean of the combined math and verbal scores is 1100, while the standard deviation is 141.

Explanation:

Normal variables

Normal variables have mean
`\mu` and standard deviation
`\sigma`

When we add normal variables, the combined mean is the sum of both means, and the standard deviation is the square root of the sum of both variances. The distribution is still normal.

In this question:

Verbal:
`\mu_(V) = 525, \sigma_(V) = 100`.

Math:
`\mu_(M) = 575, \sigma_(M) = 100`

Combined:

`\mu = \mu_(V) + \mu_(M) = 525 + 575 = 1100`

`\sigma = \sqrt{\sigma_(V)^(2)+\sigma_(M)^(2)} = √(100^2 + 100^2) = 141`

The mean of the combined math and verbal scores is 1100, while the standard deviation is 141.