In a certain dart game, a player can score either 1 for landing in the outer...
In a certain dart game, a player can score either 1 for landing in the outer ring, 3 for landing in the middle ring, and 5 for landing in the inner ring. Assume a player makes 60 throws, and assume they have an equal chance of hitting each ring. What is the chance the player scores at least 200 points?
Homework Answers
| x | f(x) | xP(x) | x2P(x) |
| 1 | 1/3 | 0.333 | 0.3333 |
| 3 | 1/3 | 1.000 | 3.0000 |
| 5 | 1/3 | 1.667 | 8.3333 |
| total | 3.0000 | 11.6667 | |
| E(x) =μ= | ΣxP(x) = | 3.0000 | |
| E(x2) = | Σx2P(x) = | 11.6667 | |
| Var(x)=σ2 = | E(x2)-(E(x))2= | 2.6667 | |
| std deviation= | σ= √σ2 = | 1.6330 |
expected score for 60 throws =60*3 =180
and standard deviation =1.633*sqrt(60)= 12.649
therefore from Normal approximation:
chance the player scores at least 200 points:
P(X>200)=P(Z>(200-180)/12.649)=P(Z>1.58)=0.0569
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