A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 45.0 and 55.0 minutes. Find the probability that a given class period runs between 50.25 and 51.0 minutes. Find the probability of selecting a class that runs between 50.25 and 51.0 minutes. (Round to three decimal places as needed.)

To find the probability that a given class period runs between 50.25 and 51.0 minutes in a uniform distribution between 45.0 and 55.0 minutes, we can use the formula for uniform probabilities: \[ P = \frac{x - a}{b - a} \] where \( x \) is the upper limit, \( a \) is the lower limit, and \( b \) is the total range. Here, \( a = 45.0 \), \( b = 55.0 \), and we want the interval from \( 50.25 \) to \( 51.0 \). 1. Calculate the length of the interval: Difference in upper and lower limits \( = 51.0 - 50.25 = 0.75 \). 2. Calculate the total range of the distribution: \( b - a = 55.0 - 45.0 = 10.0 \). 3. Now we find the probability: \[ P = \frac{0.75}{10.0} = 0.075 \] So the probability that a class runs between 50.25 minutes and 51.0 minutes is 0.075. **Rounded to three decimal places, the probability is 0.075.**