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

Answer:

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

Step-by-step explanation:

Given -

Mean $(\nu )$  = 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 =

$P(2< X< 6)$   =  $P(\frac{2 - 4 }{1.5}< \frac{X - \nu }{\sigma}< \frac{6 - 4 }{1.5})$

                         = $P(\frac{-2 }{1.5}< Z< \frac{2 }{1.5})$     Put  [$Z = \frac{X - \nu }{\sigma}$]

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

                          = $(Z< 1.33) - (Z< -1.33)$

                          = .9082 - .0918

                           = 0.8164