A person who travels regularly on the 9:00 am bus from Oakland to San Francisco reports that the bus is almost always a few minutes late but rarely more than five minutes late. The bus is never more than two minutes early, although it is on very rare occasions a little early.
(a) Sketch a density function, p(t), where t is the number of minutes that the bus is late. Shade the region under the graph between t = 2 minutes and t = 4 minutes. Explain what this region represents.
(b) Now sketch the cumulative distribution function P(t). What measurement(s) on this graph correspond to the area shaded? What do the inflection point(s) on your graph of P correspond to on the graph of p? Interpret the inflection points on the graph of P without referring to the graph of p.