A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 47.0 and 57.0 minutes. Find the probability that a given class period runs between 50.75 and 51.0 minutes. Find the probability of selecting a class that runs between 50.75 and 51.0 minutes. \( \square \) (Round to three decimal places as needed.)

Let the length of a class period be the random variable \( X \) that is uniformly distributed on the interval \([47.0, 57.0]\). The probability density function (pdf) of a uniform distribution on an interval \([a, b]\) is given by \[ f(x) = \frac{1}{b-a}, \quad \text{for } a \leq x \leq b. \] Here, \( a = 47.0 \) and \( b = 57.0 \), so the pdf becomes \[ f(x) = \frac{1}{57.0 - 47.0} = \frac{1}{10}. \] We need to find the probability that \( X \) falls between \( 50.75 \) and \( 51.0 \) minutes. This probability is given by \[ P(50.75 \leq X \leq 51.0) = \int_{50.75}^{51.0} \frac{1}{10} \, dx. \] Since the pdf is constant, the integral simplifies to \[ P(50.75 \leq X \leq 51.0) = \frac{1}{10} (51.0 - 50.75) = \frac{1}{10} \times 0.25 = 0.025. \] Thus, the probability that a given class period runs between \( 50.75 \) and \( 51.0 \) minutes is \[ \boxed{0.025}. \]