Your company has been contracted to organise a K-pop concert at Sydney Olympic Park in September. However, the month of September comes with a lot of rain. Your role as the consultant is to evaluate the risk involved in holding the concert. After consulting with the bureau of meteorology that ranks the weather as 'terrible', 'good', or 'great', you have some estimates of attendance (in thousands). Your estimates show that there is a 20% chance of 'terrible' weather, in which case only 50 (thousand) people will attend the concert. There is 60% chance of 'good' weather, which in which case 80 (thousand) people will attend the concert, and if the weather is great, 100 (thousand) people will attend the concert. Suppose that tickets sell for $5 each and that the total cost for organizing the concert is a fixed $10,000. If profit is defined as the difference between total sales revenue and total cost, the standard deviation of the profit is _________.
Question
Your company has been contracted to organise a K-pop concert at Sydney Olympic Park in September. However, the month of September comes with a lot of rain. Your role as the consultant is to evaluate the risk involved in holding the concert.
After consulting with the bureau of meteorology that ranks the weather as 'terrible', 'good', or 'great', you have some estimates of attendance (in thousands). Your estimates show that there is a 20% chance of 'terrible' weather, in which case only 50 (thousand) people will attend the concert. There is 60% chance of 'good' weather, which in which case 80 (thousand) people will attend the concert, and if the weather is great, 100 (thousand) people will attend the concert.
Suppose that tickets sell for 10,000.
If profit is defined as the difference between total sales revenue and total cost, the standard deviation of the profit is _________.
Solution
To calculate the standard deviation of the profit, we first need to calculate the expected profit and the variance of the profit.
Step 1: Calculate the expected profit
The expected profit is calculated by multiplying the probability of each outcome by the profit for that outcome, and then summing these values.
Profit for 'terrible' weather = (50,000 * 10,000 = 5) - 390,000 Profit for 'great' weather = (100,000 * 10,000 = $490,000
Expected profit = (0.20 * 390,000) + (0.20 * 372,000
Step 2: Calculate the variance of the profit
The variance is calculated by subtracting the expected profit from the profit for each outcome, squaring the result, multiplying by the probability of each outcome, and then summing these values.
Variance = (0.20 * (372,000)^2) + (0.60 * (372,000)^2) + (0.20 * (372,000)^2)
Step 3: Calculate the standard deviation of the profit
The standard deviation is the square root of the variance.
So, we need to calculate the variance first to find the standard deviation.
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