Calculation practice: Finding the probability of a range of values using the normal distribution. The natural log of growth (change in radius per year in mm) of Engelmann spruce is approximately normally distributed with mean of 0.037 log units and standard deviation 0.385. Following these steps, determine the probability that a tree has a bad year, defined as having growth less than −0.050 log units in a year.

a. Make a sketch of the normal distribution with mean 0.037, and mark the values that we are trying to determine (i.e., those values less than −0.05 ).

b. Calculate the standard normal deviate (Z) associated with the value we are interested in here, −0.05.

c. We are interested in the probability of getting a value less than this Z value. Is this probability directly shown in Statistical Table B? If not, what quantity can we use to find what we need?

d. What is the probability that a random draw from a standard normal distribution will be greater than 0.226?

e. What is the probability that a random draw from a standard normal distribution will be less than −0.226?

f. What is the probability that a tree has a bad growth year, that is, less than −0.050 in log units?