The payouts for the powerball lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is a dollar.
Divisions Payout Odds Probability
5+Powerball $50,023,000 146,107,978 .000000006892
Match 5 214,000 3,563,610 .000000280615
4+Powerball 18,0000 584,450 .000001710345
Match 4 170 14,215 .000070098465
3+ Pwerball 170 11, 932 . 000083059255
match 3 11 294 .003463457534
2+ powerball 11 770 . 001344582574
1+ powerball 4 139 .007829800000
0+ powerball 3 71 .014674514286
a. Find the mean and standard deviation of the payout.
b. If the cost of a ticket is taken into account then the mean is a loss of $? And the SD is changed or unchanged?