High School

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 51.6 and 51.7 minutes.

A) P(51.6 < X < 51.7) = 0
B) P(51.6 < X < 51.7) = 1
C) P(51.6 < X < 51.7) = 0.1
D) P(51.6 < X < 51.7) = 0.05

Answer :

Final answer:

The probability that the professor's class duration is between 51.6 and 51.7 minutes is 0.05.

Explanation:

To find the probability that the professor's class duration is between 51.6 and 51.7 minutes, we need to calculate the area under the probability density function (PDF) curve between these two values.

Given that the class duration has a continuous uniform distribution between 50.0 minutes and 52.0 minutes, the probability density function is a constant value of 1/(52.0 - 50.0) = 1/2.

The area under the PDF curve between 51.6 and 51.7 minutes is equal to the width of the interval (51.7 - 51.6) multiplied by the height of the PDF curve (1/2). So, P(51.6 < X < 51.7) = (51.7 - 51.6) * (1/2) = 0.05.

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