Question

Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $7$ on them and the other two have a $2$ on them.

How many $2$'s do we have to add to make the expected value equal to $4$?

Answer 1

Let x be the number of 2's added. The new mean is (60 + 2x)/(10 + x), since the original total is 60. Set this equal to 4:

(60 + 2x)/(10 + x) = 4
60 + 2x = 40 + 4x
20 = 2x
x = 10.

So you must add 10 slips showing 2.