statistics midterm review #43

Question

Bus wait times are uniformly distributed between 15 minutes and 20 minutes. The unshaded rectangle below with area 1 depicts this. The shaded rectangle depicts the probability that a randomly selected bus wait time will be between 17 and 19 minutes. Give answers to the following questions in fraction form.

The boxplot is shaded from 17 through 19

14 15 16 17 18 19 20 21

Answer 1

If the event space is discrete and bounded by the numbers 15 and 20 there are 6 possible outcomes {15, 16, 17, 18, 19, 20}. If the probability distribution is uniform than the chance of any one wait time would be 1/6. The total possible wait times being examined are {17, 18, 19}. Thus the total probability that a wait time would be one of these values would be 3 * 1/6 or 3/6 in fraction form. Simplified that would be 1/2.