Question

Statistic Problem In a lottery conducted to benefit the local fire company, 8000 tickets are to be sold at $4 each. The prize is a $12,000 automobile. If you purchase three tickets, (Hint: Subtract the amount spent for the tickets) a.) Let x be the net amount won or lost. What are the values of the two different outcomes? b.) Create a probability distribution for the two outcomes above. c.) Find the expected value and the standard deviation.

Answer 1

a.) Let x be the net amount won or lost. What are the values of the two different outcomes?

In case of Loss = 3*$4 = -$12

In case of win = $12000 - 3*$4 = $12000 - $12 = $11988

b.) Create a probability distribution for the two outcomes above.

P[ winning ] = 3/8000 ( he bought 3 tickets )

P[ loosing ] = 1 - 3/8000

P[ loosing ] = 7997/8000

X	P(X)
-12	7997/8000
11988	3/8000
Total	1

c) c.) Find the expected value and the standard deviation.

E(X) = ( 7997/8000 )* (-12 ) + (3/8000 )*11988

E(X) = 35964/8000 - 95964/8000

E(X) = -60000/8000

E(X) = -$7.5

E(X^2) = ( 7997/8000 )* (-12 )^2 + (3/8000 )*11988^2

E(X^2) = 1151568/8000 + 431136432/8000

E(X^2) = 432288000/8000

E(X^2) = 54036

V(X) = E(X^2) - E(X)^2

V(X) = 54036 - (7.5)^2

V(X) = 54036 - 56.25

V(X) = 53979.75

Sd(X) = 232.33