Answer-first summary for fast verification
Answer: $8,500
## Explanation To compute the bonus, we apply the following linear transformation to each employee's salary: \[ Y = \alpha + \beta X \] \[ Y = 1,000 + 0.15X \] where: - Y is the transformed variable (bonus) - X is the original variable (salary) - β is the scale constant (0.15) - α is the shift constant ($1,000) The mean bonus, i.e., mean of Y, is given by: \[ E(Y) = E(\alpha + \beta X) = \alpha + \beta E(X) \] We know that the mean salary is $50,000. Thus: \[ E(Y) = \$1,000 + 0.15(\$50,000) \] \[ E(Y) = \$1,000 + \$7,500 \] \[ E(Y) = \$8,500 \] Therefore, the mean bonus received by employees is **$8,500**.
Author: Tanishq Prabhu
Ultimate access to all questions.
No comments yet.
The average salary for an employee at Capital Asset Managers is $50,000 per year. This year, the management has decided to award bonuses to every employee:
$1,000Determine the mean bonus received by employees.
A
$8,500
B
$4,250
C
$500
D
$10,500