One state lottery has 1,100 prizes of $1; 105 prizes of $10; 25 prizes $50; 5 pr
ID: 3368727 • Letter: O
Question
One state lottery has 1,100 prizes of $1; 105 prizes of $10; 25 prizes $50; 5 prizes of $280; 2 prizes of $1,190; and 1 prize of $2,300. Assume that 36,000 lottery tickets are issued and sold for $1. 1. What is the lottery’s expected profit per ticket? 2. What is the lottery’s standard deviation of profit per ticket? One state lottery has 1,100 prizes of $1; 105 prizes of $10; 25 prizes $50; 5 prizes of $280; 2 prizes of $1,190; and 1 prize of $2,300. Assume that 36,000 lottery tickets are issued and sold for $1. 1. What is the lottery’s expected profit per ticket? 2. What is the lottery’s standard deviation of profit per ticket? 1. What is the lottery’s expected profit per ticket? 2. What is the lottery’s standard deviation of profit per ticket?Explanation / Answer
Here first let find the distribution of X which is the profit per ticket.
The possible value of X's are $0, $9, $49, $179, $1189, $2299 and -$1.
The corresponding probabilities and necessary calculations,
1) Mean = -0.75056
2) SD = [ 232.6761 - (-0.75056)2 ]1/2 = 15.23525.
Profit(Xi) Freq Probability(Pi) XiPi Xi2Pi 0 1100 0.030555556 0 0 9 105 0.002916667 0.02625 0.23625 49 25 0.000694444 0.034028 1.667361 179 5 0.000138889 0.024861 4.450139 1189 2 5.55556E-05 0.066056 78.54006 2299 1 2.77778E-05 0.063861 146.8167 -1 34762 0.965611111 -0.96561 0.965611 Total 36000 1 -0.75056 232.6761Related Questions
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