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 $\times 3.7 = 11.1$ minutes.The standard deviation of your wait time is $2.12+2.12+2.12≈3.64\sqrt { 2.1 ^ { 2 } + 2.1 ^ { 2 } + 2.1 ^ { 2 } } \approx 3.64$ 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

Question

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

\times 3.7 = 11.1

minutes.The standard deviation of your wait time is

2.12+2.12+2.12≈3.64\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

Talal Alruwaily · Accepted Answer

Final Answer : C, Explanation :  For the mean calculation, no assumptions about the distribution or independence of service times are required because the mean of the sum is simply the sum of the means. For the standard deviation calculation, the assumption is that the service times are independent, allowing the variances to be added and the square root taken to find the overall standard deviation. The normality assumption is not explicitly required for these calculations.

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