Check my answers please, thank you! One state lottery has 1,200 prizes of $1; 12
ID: 3302837 • Letter: C
Question
Check my answers please, thank you!
One state lottery has 1,200 prizes of $1; 125 prizes of $10; 25 prizes of $65; 5 prizes of $280; 2 prizes of $1,240; and 1 prize of $2,600. Assume that 37,000 lottery tickets are issued and sold for $1. Question 1 is the lottery's expected profit per ticket? 0.7147 Question 2What is the lottery's standard deviation of profit per ticket? 16.7352 deceased from a According to the Centers or Disease Control and Prevention, heart disease causes 35% o U.S. were examined for cause of death deaths the United States Suppo e asa e o 13 ecent s e Question 3 Find the probability that between 5 and 10, exclusive, of the recently deceased died due to heart disease. 0.2816 Question 4 Find the probability that less than 4 of the recently deceased died due to heart disease. 0.2783Explanation / Answer
1. The expected cost price: sigma (number of prizes*prize amount)=1*1200+125*10+25*65+5*280+2*1240+1*2600=$10555; the expected selling price: 37000*1=37000.
Expected Profit=selling price-cost price=37000*1-10555=$26445
Expected Profit per ticket=26445/37000=$0.7147
2. Lottery' sstandard deviation of profit per ticket=sqrt[1/37000-1{(1-0.7147)^2*1200+...+(2600-0.7147)^2*1}]=16.71 [using formula s=sqrt[1/n-1 sigma (xi-xbar)^2]
3. There are n=13 independent trials, and probability of success, p=0.35. The probability of success is constant throughout the trials, thus use binomial distribution table (n=13, p=0.35) to find the required probability.
P(5<X<10)=P(X<10)-P(X<5)=P(X<=9)-P(X<=4)=0.9975-0.5005=0.497 (ans)
4. P(X<4)=P(X<=3)=0.2783