Question

Let XX represent the full height of a certain species of tree. Assume that XX has a normal probability distribution with μ=182.9μ=182.9 ft and σ=7.1σ=7.1 ft.

You intend to measure a random sample of n=87n=87 trees.

What is the mean of the distribution of sample means?
μ¯x=μx¯=

What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)?
(Report answer accurate to 4 decimal places.)
σ¯x=

σx¯=

Answer 1

Solution :

Given that ,

mean = $\mu$ = 182.9

standard deviation = $\sigma$ = 7.1

n = 87

$\mu$_{$\bar x$} = 182.9

$\sigma$_{$\bar x$} = $\sigma$ / $\sqrt$ n = 7.1/ $\sqrt$ 87 = 0.7612