The State Department of Forests has determined that annual tree growth in a particular forest area is normally distributed with a mean equal to 17 inches and a standard deviation equal to 6 inches. If 2 trees are randomly chosen, the probability that both trees will have grown more than 20 inches during the year is approximately .037.

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To find the probability that a tree has grown more than 20 inches, we first calculate the Z-score for 20 inches using the formula Z = (X - μ) / σ, where X is the value (20 inches), μ is the mean (17 inches), and σ is the standard deviation (6 inches). This gives us a Z-score of (20-17)/6 = 0.5. Looking up this Z-score in a standard normal distribution table or using a calculator, we find the probability of a single tree growing more than 20 inches is approximately 0.3085. The probability that both of two independent trees have grown more than 20 inches is the square of this single probability (since the trees' growths are independent events), which is 0.3085^2 ≈ 0.0952, not 0.037.

The State Department of Forests Has Determined That Annual Tree