. Concert attendance depends on the weather. There are three possible types of w
ID: 1169369 • Letter: #
Question
. Concert attendance depends on the weather. There are three possible types of weather on the day of the concert: terrible, with probability 20%, mediocre, with probability 60%, and great, with probability 20%. Concert attendance is expected to be 500 people if the weather is terrible, 1000 people if the weather is mediocre, and 2000 people if the weather is great. Let X denote the attendance.
(a) What is the expected attendance, E(X)?
(b) Suppose that each ticket costs $5 and the total cost of giving the concert is fixed and equal $2000. Then, if Y denotes profit from the concert, we have Y = 5X 2000. What is the expected profit?
(c) Find the standard deviation of profit Y .
Explanation / Answer
(a) Expected attendance E(X) = 20%(500) + 60%(1000) +20% (2000) = 100 + 600 + 400 = 1100
(b) Y= 5X-2000
X= 1100 as the expected attendance
Y= 5(1100)-2000 = 3500
(c)
three cases :
Under terrible weather , Y= 5(500)-2000 =500
Under medicore weather, Y = 5(1000)-2000 = 3000
Under great weather , Y=5(2000)-2000 = 8000
Under expected probability = 3500
Use excel function STDEV (RANGE OF VALUES) = STDEV (500,3000,8000,3500) = 3,122.49
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