Question

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with μ = 151.5 ft and σ = 97.7 ft. You intend to measure a random sample of n = 226 trees.
What is the mean of the distribution of sample means?
μ¯x =

What is the standard deviation of the distribution of sample means (i.e., the standard error in estimating the mean)?
σ¯x =

Report your answers rounded to 4 decimal places.

Answer 1

The mean of the random samples is the same as the mean of X, µ = 151.5.

The standard error is the standard deviation of X divided by the square root of the sample size, σ = 97.7/√226 ≈ 6.6320.