Two hundred draws will be made at random with replacement from the box
(a) If the sum of the 200 numbers drawn is $30,$ what is their average?
(b) If the sum of the 200 numbers drawn is $-20,$ what is their average?
(c) In general, how can you find the average of the draws if you are told their sum?
(d) There are two alternatives:
(i) winning $1 if the sum of the 200 numbers drawn is between $-5$ and $+5 .$
(ii) winning $1 if the average of the 200 numbers drawn is between $-0.025$ and $+0.025 .$
Which is better, or are they the same? Explain.