A continuous variable x is said to have a uniform distribution of the density function is given by

f(x) = 1/(b-a) a

The corresponding density “curve” has constant height over the interval from a to b. Suppose the time (min) taken by a clerk to process a certain application form has a uniform distribution with a = 4 and b = 6.

(a) Draw the density curve, and verify that the total area under the curve, and verify that area under the curve is indeed 1.

(b) In the long run, what proportion of forms will take between 4.5 min and 5.5 min to process? At least 4.5 min to process?

(c) What value separates the slowest 50% of all processing times from the fastest 50% (the median of the distribution)?

(d) What value separates the best 10% of all processing times from the remaining 90%?