
Explanation:
Let the random variable represent the sales brought in. We are given the variance of sales: . The compensation is calculated as a constant base salary plus a proportion of sales:
Using the properties of variance, adding a constant does not change the variance, but multiplying by a constant scales the variance by the square of that constant:
The standard deviation is the square root of the variance:
Rounding to the nearest whole number gives \`112`$.
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Q.63 At Capital Bank, the compensation framework comprises a basic salary plus bonuses. The average salary among sales employees is $30,000 per year, and they are also entitled to a bonus of $0.05 for every dollar of sales brought in. Average sales amount to $300,000 per year with a variance of 5,000,000. Determine the standard deviation of compensation received by employees.
A
$165
B
$450
C
$222
D
$112