Stat 366 Lab 8 Problems (November 2, 2006) page 1
Sampling Distributions Related to the Normal Distribution
7.3 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 these measurements (in square inches) to be normally
distributed with standard deviation approximately 4 square inches. If the forester samples
n= 9 trees, find the probability that the sample mean will be within 2 square inches of the
population mean.
7.4 Suppose the forester in Exercise 7.3 would like the sample mean to be within 1 square inch
of the population mean, with probability .90. How many trees must he measure in order to
ensure this degree of accuracy?
The Central Limit Theorem
7.28 An important aspect of a federal economic plan was that consumers would save a substantial
portion of the money that they received from an income tax reduction. Suppose that early
estimates of the proportion of total tax saved, based on a random sampling of 35 economists,
had mean 26% and standard deviation 12%.
(a) What is the approximate probability that a sample mean estimate, based on a random
sample of n= 35 economists, will lie within 1% of the mean of the population of the
estimates of all economists?
(b) Is it necessarily true that the mean of the population of estimates of all economists is
equal to the percent tax saving that will actually be achieved?
7.33 One-hour carbon dioxide concentrations in air samples from a large city average 12 ppm (parts
per million) with standard deviation 9 ppm.
(a) Do you think that carbon monoxide concentrations in air samples from this city are
normally distributed? Why or why not?
(b) Find the probability that the average concentration in 100 randomly selected samples
will exceed 14 ppm.
