Answer:
Proportion of the trees will have diameters between 2 and 6 inches = 0.8164
Step-by-step explanation:
Given -
Mean [tex](\nu )[/tex] = 4
Standard deviation [tex](\sigma )[/tex] = 1.5
Let X be the diameter of tree
proportion of the trees will have diameters between 2 and 6 inches =
[tex]P(2< X< 6)[/tex] = [tex]P(\frac{2 - 4 }{1.5}< \frac{X - \nu }{\sigma}< \frac{6 - 4 }{1.5})[/tex]
= [tex]P(\frac{-2 }{1.5}< Z< \frac{2 }{1.5})[/tex] Put [[tex]Z = \frac{X - \nu }{\sigma}[/tex]]
= [tex]P(-1.33< Z< 1.33)[/tex]
= [tex](Z< 1.33) - (Z< -1.33)[/tex]
= .9082 - .0918
= 0.8164
