This Question: 1 pt 20 of 20 (1 complete) This Test: 20 pts poss 1 Use the fact

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This Question: 1 pt 20 of 20 (1 complete) This Test: 20 pts poss 1 Use the fact that the mean of a geometric distribution is - and the variance is 2 Letx be the number of times you play A daily number lottery chooses two balls numbered 0 to 9. The probability of winning the lottery is 100 winning the first time. (a) Find the mean, variance, and standard deviation. (b) How many times would you expect to have to play the lottery before winning? It costs $1 to play and winners are paid $500. Would you expect to make or lose money playing this lottery? Explain the lottery before (a) The mean is(ype n integer or a decimal.) The variance is. (Type an integer or a decimal.) The standard deviation is 11. Round to one decimal place as needed.) (b) You can expect to play the game times before winning. Would you expect to make or lose money playing this lottery? Explain. 0 A You would expect to make money. On average you would in $500 once in every 0 B. You would expect to lose money. On average you would win $500 once in every times you play. So the net gain would be $ times you play So the net gain would be s

Explanation / Answer

p = 1/100 = 0.01

(a)
mean = 1/p = 1/0.01 = 100

variance = (1-p)/p^2 = (1-0.01)/0.01^2 = 9900

std. dev. = sqrt(variance) = sqrt(9900) = 99.4987

(b)
You can expect to play the game 100 times before winning

winnings = 500 - 100*1 = 400

You would expect to make money. On average you would win $500 once in every 100 times you play. So the net gain would be $400.

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