Note: Answer Questions 1-4 by Using your Calculator. IMPORTANT: Make sure you ca

Question

Note: Answer Questions 1-4 by Using your Calculator. IMPORTANT: Make sure you carry all decimals until you reach your answer, then round to four decimals. 10 12 13 4 One state lottery has 1,100 prizes of $1; 125 prizes of $10; 30 prizes of $50; 5 prizes of $330; 2 prizes of $1,210; and 1 prize of $2,600. Assume that 24,000 5 lottery tickets are issued and sold for $1. 16 17 18 19 20 21 Question 1 What is the lottery's expected profit per ticket? 23 Question 2 What is the lottery's standard deviation of profit per ticket? 25 26

Explanation / Answer

1)

no of prizes of $1 = 1,100

no of prizes of $10 = 125

no of prizes of $50 = 30

no of prizes of $330 = 5

no of prizes of $1,120 = 2

no of prizes of $2,600 = 1

no of tickets with no prize = 24000 - (1100+125+30+5+2+1) = 22737

lottery's expected profit per tciket for person buying ticket= (1100/24000)($1-$1)+(125/24000)($10-$1) + (30/24000)($50-$1) +(5/24000)($330-$1)+ (2/24000)($1120-$1)+ (1/24000)($2600-$1) + (22737/24000)($0-$1)

= -$0.5692

lottery's expected profit per tciket for person buying ticket is -$0.5692

lottery's expected profit per tciket for person selling ticket is $0.5692

2)

varinace of profit per ticket =  (1100/24000)($1-$1-$0.5692 )2+(125/24000)($10-$1-$0.5692 )2+ (30/24000)($50-$1-$0.5692 )2 +(5/24000)($330-$1-$0.5692 )2+ (2/24000)($1120-$1-$0.5692 )2+ (1/24000)($2600-$1-$0.5692 )2 + (22737/24000)($0-$1-$0.5692 )2 =413.6894

standard deviation of profit per ticket = varinace = 413.6894 = 20.3393

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