Question

Jessica is waiting for a subway. If X is the amount of time before the next subway arrives, and X is uniform with values between 13 and 19 minutes, then what is the approximate standard deviation for how long she will wait, rounded to one decimal place

Answer 1

The approximate standard deviation for how long Jessica will wait for the subway is approximately 2.45 minutes.

Step-by-step explanation:

To find the approximate standard deviation for how long Jessica will wait for the subway, we need to use the formula for the standard deviation of a uniform distribution, which is:

standard deviation = (b - a) / sqrt(12)

In this case, a = 13 and b = 19 (the range of possible values for X, the amount of time before the next subway arrives). Plugging these values into the formula, we get:

standard deviation = (19 - 13) / sqrt(12) ≈ 2.45 minutes

Therefore, the approximate standard deviation for how long Jessica will wait is approximately 2.45 minutes.

Answer 2

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.