A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 50.0 and 55.0 minutes. Find the probability that a given class period runs between 51.5 and 51.75 minutes. Find the probability of selecting a class that runs between 51.5 and 51.75 minutes. \( \square \) (Round to three decimal places as needed.)

To find the probability that a given class period runs between 51.5 and 51.75 minutes when the lengths are uniformly distributed between 50.0 and 55.0 minutes, we can use the formula for the probability of a uniform distribution: \[ P(a \leq X \leq b) = \frac{b - a}{d - c} \] where \( [c, d] \) is the range of the distribution, and \( [a, b] \) is the range for which we want to find the probability. In this case, \( c = 50.0 \), \( d = 55.0 \), \( a = 51.5 \), and \( b = 51.75 \). Plugging in the values: \[ P(51.5 \leq X \leq 51.75) = \frac{51.75 - 51.5}{55.0 - 50.0} \] \[ P(51.5 \leq X \leq 51.75) = \frac{0.25}{5.0} = 0.05 \] So, the probability that a class lasts between 51.5 and 51.75 minutes is \( \boxed{0.050} \) (rounded to three decimal places).