Consider the following to answer the question(s) below:
A company believes that there will be a 50% chance of making a profit of $1,000, a 30% chance of making a profit of $1500 and a 20% chance of making a profit of $2,000.
-Find the standard deviation for the company's profit?
A) $390.51
B) $152,498
C) $350
D) $18.71
E) $1,350

Question

Quizplus · Accepted Answer

To find the standard deviation of the profits, we need to first find the expected value (mean) of the profits.

Expected value = (0.5 x $1000) + (0.3 x $1500) + (0.2 x $2000) = $1350

Now we will find the variance:

Variance = (0.5 x ($1000-$1350)^2) + (0.3 x ($1500-$1350)^2) + (0.2 x ($2000-$1350)^2) 
         = $390,510

Finally, we take the square root of the variance to get the standard deviation:

Standard deviation = √($390,510) = $390.51

Therefore, the answer is A) $390.51.

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