50. The article cited in Example 1.20 proposed the lognormal distribution with 5 4.5 and 5 .625 as a model for total hydrocarbon emissions (g/gal).

a. What proportion of engines emit at least 50 g/gal? Between 50 and 150 g/gal?

b. What value c separates the best 1% of engines with respect to THC emissions from the remaining 99%?

51. The article "On Assessing the Accuracy of Offshore Wind Turbine Reliability-Based Design Loads from the Environmental Contour Method" (Intl. J. of Offshore and Polar Engr., 2005: 132-140) proposes the Weibull distribution with 5 1.817 and 5 .863 as a model for 1-hour significant wave height (m) at a certain site.

a. What proportion of wave heights are at most 0.5 m?

b. What proportion of wave heights are between 0.2 and 0.6 m?

c. What is the 90th percentile of the wave height distribution? The 10th percentile?

54. On his way to work, a friend of ours must pass through ten traffic signals. Suppose that in the long run, she encounters a red light at 40% of these signals and that whether any particular signal is red is independent of whether any other one is red.

a. On what proportion of days will our friend encounter at most two red lights? At least five red lights?

b. On what proportion of days will our friend encounter between two and five (inclusive) red lights?

59. Let x denote the number of trees in a quarter-acre plot within a certain forest. Suppose that x has a Poisson distribution with 5 20 (corresponding to an average density of 80 trees per acre). In what proportion of such plots will there be at least 15 trees? At most 25 trees?