Question

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 36.4 ft and standard deviation 39.6 ft.You intend to measure a random sample of n=97 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 following, correct to two decimal places.
μ¯x = ________.σ¯x = ________.

Answer 1

Answer:

μ¯x = 36.4 ft

σ¯x = 4.02

Step-by-step explanation:

μ = 36.4 ft

σ = 39.6 ft

n = 97 trees

The mean of a sampling distribution will be the mean of the population/probability distribution. So in this example, it would be 36.4 feet.

μ¯x = μ = 36.4 ft

The standard deviation of the sampling distribution, what is also referred to as standard error, is the standard deviation of the population/probability distribution divided by the square root of the sample size (n). So in this example, it would be 39.6 divided by the square root of 97:

σ¯x = σ / √n   ⇒   σ¯x = 39.6 / √97 = 4.02