Final answer:
To find the maximum diameter in the bottom 8% of the population, calculate the z-score and use it to find the corresponding diameter.
Step-by-step explanation:
To find the maximum diameter a Douglas fir can have and still be in the bottom 8%, we need to find the z-score corresponding to the bottom 8% of the normal distribution. The z-score can be found using the cumulative standard normal distribution table or a calculator. In this case, the z-score is approximately -1.405.
Next, we can use the formula for z-scores to find the corresponding diameter:
diameter = mean + (z-score * standard deviation)
Substituting the values, we get:
diameter = 50 cm + (-1.405 * 12 cm) = 32.78 cm
Therefore, the maximum diameter a Douglas fir can have and still be in the bottom 8% is approximately 32.78 cm.