Statistics - Uniform Distribution

Question

The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 51.7 and 51.8 min.

P(51.7 < X < 51.8) =

Answer 1

Probability of this event is 0.05

The continuous uniform distribution has domain [50, 52]. For a uniform distribution, the density function must be constant on this domain. Because it's a probability distribution, it must integrate to 1.

We need a constant c such that ∫cdt = 1, where the lower limit of integration is 50 and the upper limit is 52. Therefore c = 1/2.

P(51.7 < X < 51.8) = 1/2∫dt, where the lower limit of integration is now 51.7 and the upper limit is 51.8. Answer is 1/2 * 0.1