Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 139 ft and standard deviation 10.7 ft.

Question

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 139 ft and standard deviation 10.7 ft. You intend to measure a random sample of n=35 trees. The bell curve below represents the distribution 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.

(the boxes are each two tick marks away from the mean.)

μ¯x =

σ¯x=

Answer 1

Hi Kristen,

The mean of a sampling distribution will be the mean of the population/probability distribution. So in this example, it would be 139 feet.

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 10.7 divided by the square root of 35.

Please let me know if that explanation helps or if you have any other questions.

Best,

Mike