Jen's commute to work requires that she take the blue subway line, then transfer to the red line. the length of the trip on the blue line has a mean of 18 minutes with a standard deviation of 2 minutes. the red line trip takes 12 minutes with a standard deviation of 1 minute. the waiting time between when she gets off the blue line and her red line train arrives has mean of 10 minutes and a standard deviation of 5 minutes. assume (perhaps unrealistically) that these times are independent random variables. what are the mean and standard deviation of her entire commute?

Question

Mathematics

Tori Gregory

21 September, 18:35

Jen's commute to work requires that she take the blue subway line, then transfer to the red line. the length of the trip on the blue line has a mean of 18 minutes with a standard deviation of 2 minutes. the red line trip takes 12 minutes with a standard deviation of 1 minute. the waiting time between when she gets off the blue line and her red line train arrives has mean of 10 minutes and a standard deviation of 5 minutes. assume (perhaps unrealistically) that these times are independent random variables. what are the mean and standard deviation of her entire commute?

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Answers (1)

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Molly Mayer · Answer 1

In order to combine the mean and standard deviations of multiple independent variables, you simply sum the means together and you sum the variances together. Since the standard deviation is the square root of the variance, what you actually do is you take the square root of the sum of the squares of the standard deviations. So:

Means:

18 + 12 + 10 = 40

Standard deviations

sqrt (2^2 + 1^2 + 5^2) = sqrt (4 + 1 + 25) = sqrt (30) = 5.477225575

So, for Jen's entire commute, the mean is 40 minutes with a standard deviation of 5.5 minutes.