standard deviation?

[soyleaf]

A set of scores has mean 70.3 and a standard deviation 8.8. The scores are now scaled according to the formula y = 0.7x + 30, where x is the old score and y is the new score. What is the standard deviation of the new scores? (A) 4.31 (B) 6.16 (C) 7.36 (D) 36.16 (E) 37.36

im really not sure where to go with this please help

 

[Dr.Peterson]

Have you been taught anything about how such transformations affect mean and standard deviation? There is a fairly simple theorem you might know have been taught.

Or, you might be expected to use the definitions to ponder what will happen if you replace every score x in the set with a new score 0.7x + 30 .

I can't tell which you are expected to do, without knowing your context. Maybe you can tell us what facts were taught in your current lesson.

 

[Steven G]

Suppose you play a game where you win some money. Let X be the RV representing how much you win. Suppose E(X) = $k

So each time you play this game you expect to win $k. If you prefer replace k with any number of your choice.

Business is a bit slow so the game company has a special where all their payoffs will be doubled. How much would you expect to win on each game now? What would E(X) be if they now say that they are only going to pay 70% of what they were originally offering?

What if they say that they will payouts will all be increased by $30 for each game you played. Do you see that E(X) will now be $(k+30).

Use these ideas to find the SD.