Current learning objective: The Uniform Distribution Question 16 Score: 0 of 4 points The duration of a professor's class has a continuous uniform distribution between 50.0 minutes and 52.0 minutes. If one class is randomly selected, find the probability that the professor's class duration is between 51.8 and 51.9 minutes. \( P(51.8

Ask by Allan Rodriquez. in the United States

Mar 15,2025

To solve for the probability that the professor's class duration falls between 51.8 and 51.9 minutes given a uniform distribution, we can use the formula for continuous uniform distribution which is: \[ P(a < X < b) = \frac{b - a}{d - c} \] where \( c \) is the lower limit, \( d \) is the upper limit, and \( a \) and \( b \) are the limits of the desired interval. In this case: - \( c = 50.0 \) - \( d = 52.0 \) - \( a = 51.8 \) - \( b = 51.9 \) Thus, the calculation would be: \[ P(51.8 < X < 51.9) = \frac{51.9 - 51.8}{52.0 - 50.0} = \frac{0.1}{2.0} = 0.05 \] So, \( P(51.8 < X < 51.9) = 0.05 \). Now, simply put, the probability that the class duration is between 51.8 and 51.9 minutes is **0.05** or **5%**.