Question

We are interested in knowing how likely it is for one type of tree to grow to a certain length. The length of these trees exhibits a normal distribution. The tree that you measure is 120 cm. Given that the mean is 100 cm and the standard deviation is 10 cm, do you think this tree length is uncommon for this type of tree

Answer 1

The tree length of 120 cm is uncommon for this type of tree.

Step-by-step explanation:

The question is asking whether a tree length of 120 cm is uncommon for a certain type of tree, given that the mean length is 100 cm and the standard deviation is 10 cm. To determine this, we can use the concept of z-scores. The formula for calculating the z-score is Z = (x - μ) / σ, where x is the value we are interested in, μ is the mean, and σ is the standard deviation.

In this case, we have x = 120 cm, μ = 100 cm, and σ = 10 cm. Plugging these values into the formula, we get Z = (120 - 100) / 10 = 2.0.

A z-score of 2.0 indicates that the tree length of 120 cm is 2 standard deviations above the mean. Generally, if a z-score falls outside the range of -2 to 2, it is considered uncommon. Therefore, in this case, the tree length of 120 cm is uncommon for this type of tree.