Solve only b & e 10. [16 points] Suppose that the diameter at breast height (in

Question

Solve only b & e 10. [16 points] Suppose that the diameter at breast height (in inches) of trees of a certain type is normally distributed with = 8.5 and -2.5. Suppose that one tree of this type is selected at random. (a) Find the probability that the diameter of the tree is greater than 10 inches. [3 points] (b) Find the probability that the diameter of the tree is between 5 and 15 inches. [4 points] (c) Find the 25th percentile of the tree diameters. [3 points] (d) Between what two values are the middle 90% of tree diameters? [3 points] (e) If three trees are selected independently of each other, what is the probability that at least one of them has a diameter less than 10 inches? 13 points)

Explanation / Answer

b) Z1=(15-8.5)/2.5=2.6

Z2=(5-8.5)/2.5=-1.4

P(-1.4<z<2.6) = P(z<2.6)-P(z<-1.4)=0.9953-0.0809=0.9146 from normal tables

e) P( less than 10) = p =

Z=(10-8.5)/2.5=0.6

P(z<0.6)=0.7257

p=0.7257

P( At leat one less than 10)= 1-P( no less than 10)= 1- (1-0.7257)^3=0.9793

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