Question

1. a local business reports that the standard deviation of all the paychecks from their weekly payroll is $153.47. the owner of the business plans to give all employees a 12% raise along with a one - time $200 bonus. to determine each employees next paycheck, the following equation is used. next paycheck = 1.12(original paycheck) + 200. which of the following represents the standard deviation of the next paychecks? a) 1.12(153.47) + 200 b) 1.12(153.47) c) 1.12(153.47)^2 d) 1.12^2(153.47) e) 1.12^2(153.47)^2

Explanation:

Step1: Recall standard - deviation property

If \(Y = aX + b\) (where \(X\) is a random variable, \(a\) and \(b\) are constants), the standard deviation \(\sigma_Y=a\sigma_X\). Here, the original paycheck is \(X\) with standard - deviation \(\sigma_X = 153.47\), and the new paycheck \(Y = 1.12X+200\), where \(a = 1.12\) and \(b = 200\).

Step2: Calculate new standard - deviation

Using the formula \(\sigma_Y=a\sigma_X\), substitute \(a = 1.12\) and \(\sigma_X=153.47\) into it. We get \(\sigma_Y=1.12\times153.47\).

Answer:

B. \(1.12(153.47)\)