Solution Found!
The payouts for the Powerball lottery and their
Chapter 6, Problem 36E(choose chapter or problem)
Problem 36E
The payouts for the Powerball lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is $1.00. Find the mean and standard deviation of the payout. Hint: Don’t forget to include the cost of the ticket and its corresponding probability.
Divisions |
Payout |
Odds |
Probability |
Five plus Powerball |
$50,000,000 |
146,107,962 |
0.000000006844 |
Match 5 |
200,000 |
3,563,609 |
0.000000280614 |
Four plus Powerball |
10,000 |
584,432 |
0.000001711060 |
Match 4 |
100 |
14,255 |
0.000070145903 |
Three plus Powerball |
100 |
11,927 |
0.000083836351 |
Match 3 |
7 |
291 |
0.003424657534 |
Two plus Powerball |
7 |
745 |
0.001340482574 |
One plus Powerball |
4 |
127 |
0.007812500000 |
Zero plus Powerball |
3 |
69 |
0.014285714286 |
Questions & Answers
QUESTION:
Problem 36E
The payouts for the Powerball lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is $1.00. Find the mean and standard deviation of the payout. Hint: Don’t forget to include the cost of the ticket and its corresponding probability.
Divisions |
Payout |
Odds |
Probability |
Five plus Powerball |
$50,000,000 |
146,107,962 |
0.000000006844 |
Match 5 |
200,000 |
3,563,609 |
0.000000280614 |
Four plus Powerball |
10,000 |
584,432 |
0.000001711060 |
Match 4 |
100 |
14,255 |
0.000070145903 |
Three plus Powerball |
100 |
11,927 |
0.000083836351 |
Match 3 |
7 |
291 |
0.003424657534 |
Two plus Powerball |
7 |
745 |
0.001340482574 |
One plus Powerball |
4 |
127 |
0.007812500000 |
Zero plus Powerball |
3 |
69 |
0.014285714286 |
ANSWER:
Solution:
Step 1 of 2:
The given data is
Divisions |
Payout (x) |
Probability (p) |
Five plus Powerball |
$50,000,000 |
0.000000006844 |
Match 5 |
200,000 |
0.000000280614 |
Four plus Powerball |
10,000 |
0.000001711060 |
Match 4 |
100 |
0.000070145903 |
Three plus Powerball |
100 |
0.000083836351 |
Match 3 |
7 |
0.003424657534 |
Two plus Powerball |
7 |
0.001340482574 |
One plus Powerball |
4 |
0.007812500000 |
Zero plus Powerball |
3 |
0.014285714286 |
We have to find the mean and standard deviation of the payout.