Question

The heights of flowering cherry trees are normally distributed with a mean of 11.5 feet, and a standard deviation of 1.7 ft. find the probability that a randomly selected tree is less than 13.5 feet tall.

Answer 1

Mean (μ) = 11.5 feet

Standard deviation (σ) = 1.7 feet

First we need to find the z-score for less than 13.5 feet.

The formula of z-score is : z = (X - μ)/σ

Here X= 13.5, so z =
`((13.5-11.5))/(1.7)`

z =
`(2)/(1.7)` = 1.18

P(X < 13.5) = P(z< 1.18) =P(z< (1.1 + .08)) = 0.8810 (from z-score table)

P(X< 13.5) = 88.1% (for making percentage from decimal, we need to multiply by 100)

So, the probability that a randomly selected tree is less than 13.5 feet tall = 88.1%