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Darya [45]
3 years ago
9

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
Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
6 0

Answer:

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

Step-by-step 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}} = \sqrt{100^2 + 100^2} = 141

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

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