Peanuts, a rock and roll producer, has scheduled an outdoor Woodstock 2 concert where revenue will be donated to Goodwill. The profit of Woodstock 2 depends on the weather on that day, namely if the weather it is warm, cool, or frigid. If the weather is warm, Peanuts expects to make a $20,000 profit; if it is cool, Peanuts expects to make a $5,000 profit; if it is frigid, Peanuts expects to incur a $12,000 loss. Meteorologists estimate a probability distribution that based on the historical records for Woodstock NY, the chances of a warm day is 0.60, and the chances of a cool day is 0.25.

Required:

1. What is Woodstock 2's expected profit?

a) $ 5.000

b) $ 11,450

c) $ 13,000

d) $ 13,250

e) $ 15,050

Question

Mathematics

Schmitt

29 October, 03:40

Peanuts, a rock and roll producer, has scheduled an outdoor Woodstock 2 concert where revenue will be donated to Goodwill. The profit of Woodstock 2 depends on the weather on that day, namely if the weather it is warm, cool, or frigid. If the weather is warm, Peanuts expects to make a $20,000 profit; if it is cool, Peanuts expects to make a $5,000 profit; if it is frigid, Peanuts expects to incur a $12,000 loss. Meteorologists estimate a probability distribution that based on the historical records for Woodstock NY, the chances of a warm day is 0.60, and the chances of a cool day is 0.25.

Required:

1. What is Woodstock 2's expected profit?

a) $ 5.000

b) $ 11,450

c) $ 13,000

d) $ 13,250

e) $ 15,050

+4

Answers (1)

Know the Answer?

Damari Hicks · Answer 1

b) $ 11,450

Step-by-step explanation:

Each outcome has the following probability:

60% = 0.6 probability of a warm day. On a warm day, $20,000 profit. So 0.6 probability of a profit of $20,000.

25% = 0.25 probability of a cool day. On a cool day, $5,000 profit. So 0.25 probability of a profit of $5,000.

100 - (60+25) = 15% = 0.15 probability of a frigid day. On a frigid day, loss of $12,000. So 0.15 probability of losing $12,000.

1. What is Woodstock 2's expected profit?

We multiply each outcome by its probability.

0.6*20000 + 0.25*5000 - 0.15*12000 = 11450

The answer is b).