Question

Suppose that the diameters of oak trees are normally distributed with a mean of 4 feet...

Suppose that the diameters of oak trees are normally distributed with a mean of 4 feet and a standard deviation of 0.375 feet. What is the probability of a sampling a set of 87 oaks trees and finding their mean to differ from the population mean by less than 0.1 feet in diameter?

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Answer #1

Solution :

Given that,

mean = = 4

standard deviation = = 0.375

= / n = 0.375 / 87 = 0.0402

= P[(-0.1) / 0.0402< ( - ) / < (0.1) / 0.0402)]

= P(-2.49 < Z < 2.49)

= P(Z < 2.49) - P(Z < -2.49)

= 0.9936 - 0.0064  

= 0.9872

Probability = 0.9872

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