The average height of flowering cherry trees in a certain nursery is 10.5 feet. If the heights are normally distributed with a standard deviation of 1.5 feet, find the probability that a tree is less than 12.5 feet tall.
A) 0.73
B) 0.91
C) 0.96
D) 0.82

Question

Quizplus · Accepted Answer

We can solve this using the standard normal distribution:

z = (x - μ) / σ = (12.5 - 10.5) / 1.5 = 1.33

Using a z-table or calculator, we can find the probability that a standard normal variable is less than 1.33:

P(z < 1.33) = 0.9082

This means that the probability of a cherry tree being less than 12.5 feet tall is 0.9082, or approximately 0.91. Therefore, the best choice is B.

The Average Height of Flowering Cherry Trees in a Certain