Question

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. (Round your answers to four decimal places.) (a) What proportion of the trees will have diameters between 2 and 6 inches

Answer 1

Proportion of the trees will have diameters between 2 and 6 inches = 0.8164

Explanation:

Given -

Mean
`(\\u )` = 4

Standard deviation
`(\sigma )` = 1.5

Let X be the diameter of tree

proportion of the trees will have diameters between 2 and 6 inches =

`P(2< X< 6)` =
`P((2 - 4 )/(1.5)< (X - \\u )/(\sigma)< (6 - 4 )/(1.5))`

=
`P((-2 )/(1.5)< Z< (2 )/(1.5))` Put [
`Z = (X - \\u )/(\sigma)`]

=
`P(-1.33< Z< 1.33)`

=
`(Z< 1.33) - (Z< -1.33)`

= .9082 - .0918

= 0.8164