Ecological Applications (May 1995) published a study on the development of forests following wildfires in the Pacific Northwest. One variable of interest to the researcher was tree diameter at breast height 110 years after the fire. The population of Douglas fir trees was shown to have an approximately normal diameter distribution, with  μ = 50centimeters (cm) and σ = 12 cm.

a. Find the diameter, d, such that 30% of the Douglas fir trees in the population have diameters that exceed d.

b. Another species of tree, western hemlock, was found to have a breast height diameter distribution that resembled an exponential distribution with β = 30 centimeters. Find the probability that a western hemlock tree growing in the forest damaged by wildfire 110 years ago has a diameter that exceeds 25 centimeters.