Question

A forester studying the effects of fertilization on certain pine forests in the Southeast is interested in estimating the average basal area of pine trees. In studying basal areas of similar trees for many years, he has discovered that these measurements (in square inches) are normally distributed with standard deviation approximately 5 square inches. If the forester samples n = 16 trees, find the probability that the sample mean will be within 3 square inches of the population mean. (Round your answer to four decimal places.)

Answer 1

Solution :

Given that,

standard deviation = = 5

n = 16

= / n = 5 / 16 = 1.25

P( - 3 < < + 3)  

= P[ -3 /1.25 < ( - ) / < 3 / 1.25 )]

= P(-2.40 < Z < 2.40 )

= P(Z < 2.40 ) - P(Z < -2.40)

Using z table,  

= 0.9918 - 0.0082

= 0.9836