Final answer:
The probability that the class duration is between 51.6 and 51.7 minutes is 0.05, when the class duration follows a continuous uniform distribution between 50.0 minutes and 52.0 minutes.
Step-by-step explanation:
The probability that a professor's class duration is between 51.6 and 51.7 minutes, when the class duration has a continuous uniform distribution between 50.0 and 52.0 minutes, can be found using the formula P(a < X < b) = (b - a) / (m - n) where 'X' is the random variable representing the duration, 'a' and 'b' are the specific values between which we want to find the probability, and 'm' and 'n' are the minimum and maximum values of the uniform distribution, respectively.
For the class duration, we have:
a = 51.6 minutes
b = 51.7 minutes
m = 50.0 minutes (minimum duration)
n = 52.0 minutes (maximum duration)
Therefore, P(51.6 < X < 51.7) = (51.7 - 51.6) / (52.0 - 50.0) = 0.1 / 2 = 0.05. The correct answer is D) P(51.6 < X < 51.7) = 0.05.