Math, asked by logesh1195, 3 months ago

Suppose the diameter at breast height in.) of trees of acertain type is normally distributed with mean 88 and sigma - 2.8. as suggested in the article "Simulating allarvester Forwarder Softwood Thinning" (Forest Products May 1997 36-41)

a. What is the probability that the diameter of a randomly selected tree will be at Wille least 10 in Will exceed 10 in.? h. What is the probability that the diameter of a randomly selected tree will exceed

in.? c. What is the probability that the diameter of a randomly selected tree will be

between

5 and 10 in?

20

d. What value c is such that the interval includes 98% of all diameter values? e. If four trees are independently selected, what is the probability that at least one has a diameter exceeding to in?​

Answers

Answered by amitnrw
3

Given :  diameter at breast height in.) of trees of ascertain type is normally distributed with mean 8.8 and sigma - 2.8.  

To Find :  probability that the diameter of a randomly selected tree will exceed at least 10  inches

probability that the diameter of a randomly selected tree will be between

5 and 10 in

Solution:

mean = 8.8

SD = 2.8

z score = ( value - Mean ) /SD

value = 10

=> z score = ( 10 - 8.8)/2.8 = 0.42857

from z score table :  0.6658

probability that the diameter of a randomly selected tree will exceed at least 10  inches =   1 - 0.6658   = 0.3342

between  5 and 10 in

value = 10

=> z score = ( 10 - 8.8)/2.8 = 0.42857

from z score table :  0.6658

value = 5

=> z score = (5 - 8.8)/2.8 = -1.357

from z score table :  0.0875

between  5 and 10 in =    0.6658  - 0.0875   =  0.5783

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