The Amount of Time It Takes to Serve Each Customer $X _ { 1 }$

question 72

Multiple Choice

The amount of time it takes to serve each customer in a bank is a random variable,X,with a mean of ? minutes and a standard deviation of ? minutes.When you arrive at the bank there are three customers in front of you.If the times for the three customers are independent of one another,which of the following shows the correct method for calculating the variance of your wait time?

• A)Var( \(X _ { 1 }\) + \(x _ { 2 }\) + \(X _ { 3 }\) )= \(3 ^ { 2 }\) Var(X)= 9 \(\sigma ^ { 2 }\)
• B)Var(3X)= 3Var(X)= 3 \(\sigma ^ { 2 }\)
• C)Var( \(X _ { 1 }\) + \(X _ { 2 }\) + \(X _ { 3 }\) )= \(\sqrt { 3 }\) Var(X)= \(\sqrt { 3 }\) \(\sigma ^ { 2 }\)
• D)Var(3X)= \(3 ^ { 2 }\) Var(X)= 9 \(\sigma ^ { 2 }\)
• E)Var( \(X _ { 1 }\) + \(X_ { 2 }\) + \(X _ { 3 }\) )= Var( \(X _ { 1 }\) )+ Var( \(X _ { 2 }\) )+ Var( \(X _ { 3 }\) )= 3 \(\sigma ^ { 2 }\)