Waiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve y = 1/30 for 0 < x < 30, and y = 0 otherwise.

a. Graph the density curve of this variable.

b. Show that the area under this density curve to the left of any number x between 0 and 30 equals x/30.

What percentage of the time does John wait for the train

c. less than 5 minutes?

d. between 10 and 15 minutes?

e. at least 20 minutes?