Question

One state lottery has 900 prizes of $1; 105 prizes of $10; 25 prizes of $65; 5 prizes of $375; 2 prizes of $1,240; and 1 prize of $2,400. Assume that 33,000 lottery tickets are issued and sold for $1. Question 3 What is the lottery's expected profit per ticket? Question 4 What is the lottery's standard deviation of profit per ticket?

Answer 1

SOLUTION:

From given data,

One state lottery has 900 prizes of $1; 105 prizes of $10; 25 prizes of $65; 5 prizes of $375; 2 prizes of $1,240; and 1 prize of $2400. Assume that 33,000 lottery tickets are issued and sold for $1.

Prize (x)	Number	P(x)	x*P(x)	(x - $\mu$) 2	P(x) *(x - $\mu$) 2
0	33000-1038 =31962	0.96854	0	0.026968	0.02611958
1	900	0.02727	0.02727	0.698528	0.01904885
10	105	0.00318	0.0318	96.742568	0.30764136
65	25	0.00075	0.04875	4203.6783	3.15275872
375	5	0.00015	0.05625	140501.8619	21.075279
1240	2	0.00006	0.00012	1537192.7613	92.231565
2400	1	0.00003	0.00003	5759211.7709	172.776353
$\Sigma$ x = 4091	$\Sigma$ Num =  33000	$\Sigma$ p(x) = 1	$\Sigma$x*P(x) =0.16422	$\Sigma$(x - $\mu$) 2 =7441207.5404	$\Sigma$P(x) *(x - $\mu$)2 289.5887

Where ,

P(x) = Number / $\Sigma$ Num

Question 3 :What is the lottery's expected profit per ticket?

The lottery's expected profit per ticket = $\mu$ = $\Sigma$x*P(x) = $0.16422

Question 4 :What is the lottery's standard of deviation of profit per ticket?

The lottery's standard of deviation of profit per ticket = $\sigma$ = sqrt($\Sigma$P(x) *(x - $\mu$)² )

$\sigma$ = sqrt(289.5887)

$\sigma$ = $ 17.0173

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