Question

A researcher randomly (no bias) selects 121 trees in the forest to measure the diameter of...

A researcher randomly (no bias) selects 121 trees in the forest to measure the diameter of the trunk. If you know that the sample mean is 15 inches and the standard deviation for the entire forest is 33 inches, what is the probability distribution of the sample mean. (Hint: Use Central Limit Thereom, which says that sample mean has a normal distribution with the mean same as population and standard deviation of population standard deviation divided by square root of the sample size

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Answer #1

Given

n=121

sample mean=15 inches

standard deviation of entire forest=

probability distribution of sample mean=?

The confidence interval is sample mean margin of error

margin of error is

For a 95% confidence z=1.96

Using central limit theorem

=33/11=3

z=1.96

The confidence interval is sample mean margin of error

=15 3*1.96

=155.88

=(9.12,20.88) at 95% confidence

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