Question

Let

X
represent the full height of a certain species of tree. Assume that
X
has a normal probability distribution with mean 103.9 ft and standard deviation 73.9 ft.

You intend to measure a random sample of
n
=
180
trees. The bell curve below represents the distibution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places.

Answer 1

The calculated boundaries of the distribution is 92.98 to 114.92

How to calculate the missing and indicated values

From the question, we have the following parameters that can be used in our computation:

The mean of the normal distribution = 103.9 ft

The standard deviation = 73.9 ft

The random sample n is given as n = 180 trees.

So, we have

Standard Error, E = SD/√n

This gives

E = 73.9/√180

Evaluate

E = 5.51

Using the above as a guide, we have the following:

Upper bound = 103.9 + 2 * 5.51 = 114.92

Lower bound = 103.9 - 2 * 5.51 = 92.98

Hence, the boundaries is 92.98 to 114.92