b. He would like the sample mean to be within 1 square inch of the population mean, with probability 0.90. How many trees must he measure in order to ensure this degree of accuracy?

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.3: Special Probability Density Functions
Problem 40E: Pygmy Height The average height of a member of a certain tribe of pygmies is 3.2ft, with a standard...
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Instruction: Provide detailed solution and derivation.
1. 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 4 square inches.
a. If the forester samples n = 9 trees, find the probability that the sample mean will be within 2
square inches of the population mean.
b. He would like the sample mean to be within 1 square inch of the population mean, with probability
0.90. How many trees must he measure in order to ensure this degree of accuracy?
Transcribed Image Text:Instruction: Provide detailed solution and derivation. 1. 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 4 square inches. a. If the forester samples n = 9 trees, find the probability that the sample mean will be within 2 square inches of the population mean. b. He would like the sample mean to be within 1 square inch of the population mean, with probability 0.90. How many trees must he measure in order to ensure this degree of accuracy?
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