9. a local business reports that the standard deviation of all the paychecks from their weekly payroll is…

9. 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

9. 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

Answer

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))