A raffle sells 10,000 tickets. Each ticket is sold for $50. Below is a list of prizes and the number of that type of prize.
1 Grand Prize: Toyota Yaris - Value: $17,750
100 Second place prizes: Nintendo Switch with Games: $500
1000 Third Place Prizes: A Box of Frosted Lucky Charms: $4
A. Calculate the variance and round to 2 decimal places
B. Calculate the standard deviation and round to 2 decimal places
event | x | P(X=x) | xP(x) | x2P(x) |
grand prize | -17700 | 0.0001 | -1.770 | 31329.000 |
Games | -450 | 0.0100 | -4.500 | 2025.000 |
Box | 46 | 0.1000 | 4.600 | 211.600 |
No prize | 50 | 0.8899 | 44.495 | 2224.750 |
0 | total | 42.825 | 35790.350 | |
E(x) =μ= | ΣxP(x) = | 42.8250 | ||
E(x2) = | Σx2P(x) = | 35790.3500 | ||
Var(x)=σ2 = | E(x2)-(E(x))2= | 33956.369375 | ||
std deviation= | σ= √σ2 = | 184.27254 |
from above
A) variance =33956.37
B) standard deviation =184.27
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