1. In a study of wildfires in the Pacific Northwest one variable of interest to the researcher was tree diameter. The population of Douglas fir trees was shown to have an approximately normal diameter distribution with = 50 cm and = 12 cm.

a. What proportion of trees is expected to have a diameter less than 38 cm? Explain using empirical rules.

b. What proportion of trees is expected to have a diameter greater than 70 cm? Use tables type 1.

c. Find the diameterd such that 30% of the Douglas fir trees in the population have diameters that exceedd. Use tables type 1. Verify with Desmos.

2. Surveys indicate that 40% of the vehicles in some metropolitan areas cause excessive emissions of pollutants. Transport Canada randomly selects 50 vehicles for inspection in one of these areas. You need to determine the probability that the number of vehicles causing unnecessary pollution is more than 15 but fewer than 25.

a. Is normal approximation to this discrete binomial case reasonable? Justify.

b. Determine the parameters of the normal approximation.

c. What continuity correction must be used with normal approximation?

d. Use Normal Areas tables (type 1) to determine the required probability. Verify and compare the results for both CDF distributions on Desmos. Show the screenshot.