The Amount of Time It Takes to Serve Each Customer $3 \times 3.7 = 11.1$

The amount of time it takes to serve each customer in a bank is a random variable with a mean of 3.7 minutes and a standard deviation of 2.1 minutes.When you arrive at the bank there are three customers in front of you.The mean of your wait time is $3 \times 3.7 = 11.1$ minutes.The standard deviation of your wait time is $\sqrt { 2.1 ^ { 2 } + 2.1 ^ { 2 } + 2.1 ^ { 2 } } \approx 3.64$ minutes.What assumptions (if any) underlie the calculation of the mean? of the standard deviation?

A) Mean: that the time for each customer follows a Normal model Standard deviation: that the times for the three customers are independent of one another and that the time for each customer follows a Normal model
B) Mean: that the times for the three customers are independent of one another Standard deviation: that the times for the three customers are independent of one another
C) Mean: no assumptions required Standard deviation: that the times for the three customers are independent of one another
D) Mean: no assumptions required Standard deviation: no assumptions required
E) Mean: no assumptions required Standard deviation: that the times for the three customers are independent of one another and that the time for each customer follows a Normal model