A rock concert producer has scheduled an outdoor concert. The producer estimates
ID: 3379997 • Letter: A
Question
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 0.5Explanation / Answer
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]
************************
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+09Related Questions
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