The payouts for the Powerball lottery and their

Chapter 6, Problem 36E

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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

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.

 


 

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