The San Luis Obispo, California, Transit Program provides daily fixed-route transit service to the general public within the city limits and to Cal Poly State University’s staff and students. The most heavily traveled route schedules a city bus to arrive at Cal Poly at 8:54 a.m. The file titled Late lists plausible differences between the actual and scheduled times of arrival rounded to the nearest minute for this route.

a. Produce a relative frequency histogram for these data. Does it seem plausible the data came from a population that has a uniform distribution?

b. Provide the density for this uniform distribution.

c. Classes start 10 minutes after the hour and classes are a 5-minute walk from the drop-off point. Determine the probability that a randomly chosen bus on this route would cause the students on board to be late for class.

Assume the differences form a continuous uniform distribution with a range the same as the sample.

d. Determine the median difference between the actual and scheduled arrival times.