1 The diameters of Douglas firs grown at a Christmas tree fa

(1) The diameters of Douglas firs 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?

(2) The random variable x is known to be uniformly distributed between 10 and 20. Compute P(12<x<18).

Solution

What is the diameter of a tree such that 5% of all trees exceed this diameter so the require diameter is 4*105/100=4.2

to find P(X>4.2) where X has normal distribution with mean 4 and variance 1.5

hence P(X>4.2) =0.446965

(2) The random variable x is known to be uniformly distributed between 10 and 20. Compute P(12<x<18)=.6