Final answer:
The approximate standard deviation for the amount of time Jessica will wait for the subway, with the wait time uniformly distributed between 13 and 19 minutes, is 1.7 minutes.
Step-by-step explanation:
To calculate the standard deviation for a uniformly distributed random variable, we use the formula: standard deviation (\(\sigma\)) = \(\frac{b - a}{\sqrt{12}}\), where a and b are the minimum and maximum values the variable can take, respectively. In Jessica's case, the amount of time (X) before the next subway arrives follows a uniform distribution between 13 and 19 minutes. Therefore, a = 13 and b = 19.
To find the standard deviation, we substitute the values into the formula:
\(\sigma = \frac{19 - 13}{\sqrt{12}} = \frac{6}{\sqrt{12}} = \frac{6}{3.464} = 1.732\)
Rounding to one decimal place gives us a standard deviation of approximately 1.7 minutes.