Question

Certain trees grow such that their maximum heights are normally distributed with a mean of 15 m and a standard deviation of 3.5m. What percentage of the trees of this type are greater than 25.5m tall?

a. 2.50%
b. 0.30%
c. 0.15%
d. 2.35%

Answer 1

To find the percentage of trees taller than 25.5m, we calculate the z-score and use a z-table or calculator to find the percentage.

Step-by-step explanation:

The height of certain trees follows a normal distribution with a mean of 15m and a standard deviation of 3.5m.

To find the percentage of trees that are taller than 25.5m, we need to calculate the z-score for a height of 25.5m using the formula: z = (x - mean)/standard deviation.

Substituting the values, we get: z = (25.5 - 15)/3.5 = 2.92857.

Using a z-table or calculator, we can find that the percentage of trees taller than 25.5m is approximately 0.15%, which corresponds to option c.