Homework SourseA rock concert producer has scheduled an outdoor concert The
A rock concert producer has scheduled an outdoor concert. The producer estimates the attendance will depend on the weather according to the following table.
(a) What is the expected attendance?
answer:
What is the variance in attendance?
answer:
What is the standard deviation in attendance?
answer:
(b) If tickets cost $ 30 each and if band and administration costs are $ 245000, what is the expected profit?
answer:
What is the variance in profit?
answer:
What is the standard deviation in profit?
answer:
| Weather | Attendance | Probability |
| wet, cold | 3000 | 0.2 |
| wet, warm | 25000 | 0.2 |
| dry, cold | 30000 | 0.1 |
| dry, warm | 45000 | 0.5 |
Solution
Consider:
a)
Thus,
E(x) = Expected value = mean = 31100 [ANSWER]
Var(x) = E(x^2) - E(x)^2 = 262090000 [ANSWER]
s(x) = sqrt [Var(x)] = 16189.19393 [ANSWER]
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b)
Here,
Profit = 30x - 245000.
Thus,
E(profit) = 30E(x) - 245000 = 688000 [ANSWER]
Var(profit) = 30^2 Var(x) = 2.35881*10^11 [ANSWER]
s(profit) = 30 s(x) = 485675.8178 [ANSWER]
| x | P(x) | x P(x) | x^2 P(x) |
| 3000 | 0.2 | 600 | 1800000 |
| 25000 | 0.2 | 5000 | 1.25E+08 |
| 30000 | 0.1 | 3000 | 90000000 |
| 45000 | 0.5 | 22500 | 1.01E+09 |
