A 2-hour movie runs continuously at a local theater. You leave for the theater without first checking the show times. Use an appropriate uniform density function to find the probability that you will arrive at the theater within 4 minutes of the start of the film (before or after). Round to the nearest hundredth.
A) 0.06
B) 0.07
C) 0.93
D) 0.04

Question

Quizplus · Accepted Answer

Since the movie runs continuously for 2 hours (or 120 minutes), arriving within 4 minutes of the start of the film (either 4 minutes before or 4 minutes after) gives us an 8-minute window. The probability of arriving within this window, using a uniform distribution, is the length of the window (8 minutes) divided by the total length of the cycle (120 minutes), which is $ \frac{8}{120} = \frac{1}{15} \approx 0.07 $.

A 2-Hour Movie Runs Continuously at a Local Theater