19.07.2022 - 12:50

# 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

Question:

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 5 247,000 3,563,628 .000000282552
Four plus Powerball 10,000 584,454 .000001720846
Match 4 150 14,310 .000070596154
Three plus Powerball 150 11,940 .000082235921
Match 3 13 266 .003448657534
Two plus Powerball 13 775 .001318882574
One plus Powerball 5 125 .007825500000
Zero plus Powerball 4 61 .014370414286

Find the mean and standard deviation of the payout. (Round your mean value to 5 decimal places and standard deviation to 3 decimal places. Omit the ‘$’ sign in your response. Answers (1) • April 13, 2023 в 02:18 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). Do you know the answer? Not sure about the answer? Find the right answer to the question 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 by subject Math, and if there is no answer or no one has given the right answer, then use the search and try to find the answer among similar questions.
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