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. Divisions Payout Odds Probability Five plus Powerball $50,045,000 146,107,960 .000000006835 Match 5 247,00

The mean payout can be found by multiplying each payout by its corresponding probability, summing these products, and rounding to 5 decimal places. ($50,045,000)(.000000006835) + ($247,000)(.000000282552) + ($10,000)(.000001720846) + ($150)(.000070596154) + ($150)(.000082235921) + ($13)(.003448657534) + ($13)(.001318882574) + ($5)(.007825500000) + ($4)(.014370414286) = $0.69978 So the mean payout is $0.69978. To calculate the standard deviation, we first need to find the variance. The variance is the sum of the products of the squared differences between each payout and the mean payout, and the corresponding probabilities. Using the mean payout from above, we get: (($50,045,000 - 0.69978)^2)(.000000006835) + (($247,000 - 0.69978)^2)(.000000282552) + (($10,000 - 0.69978)^2)(.000001720846) + (($150 - 0.69978)^2)(.000070596154) + (($150 - 0.69978)^2)(.000082235921) + (($13 - 0.69978)^2)(.003448657534) + (($13 - 0.69978)^2)(.001318882574) + (($5 - 0.69978)^2)(.007825500000) + (($4 - 0.69978)^2)(.014370414286) = 4.0987e+12 Then, the standard deviation is the square root of the variance, rounded to 3 decimal places: sqrt(4.0987e+12) = 2,024,625.167 So the standard deviation of the payout is $2,024,625.167 (without the $ sign).