Beyond Common Core
Problem 30 of 45s12-030
Weekly earnings have mean $50 and SD $6. Weekly spending , independent of , has mean $30 and SD $8. What are the mean and SD of the savings ?
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Solution walkthrough1:49
- Means follow the rule for each week: dollars.
- Spread does not cancel: high earnings with low spending, or the reverse, push savings far from .
- For independent and , variances add, for and for : .
- Take the square root: . SDs combine like the legs of a right triangle.
- Traps: $14 adds the SDs, subtracts the variances, and $100 is the variance, not the SD.