Question

1. The diameters of Douglas furs grown at a Christmas tree farm are normally distributed with a mean of 4 inches and a standard deviation of 1.5 inches.

What is the diameter of a tree such that 5% of all trees exceed this diameter?

Answer 1

Let X be the diameter of Douglas furs grown at a Christmas tree farm.

We are given that

where ,

Let 5% of all the trees exceeds the diameter x₁. Such that

where

For 5%, the value of z₁ =-1.645

Therefore, 5% of all trees exceeds the diameter 1.5325 inches.