Question

Let X X represent the full length of a certain species of newt. Assume that X has a normal probability distribution with mean 216.4 inches and standard deviation 5 inches.

You intend to measure a random sample of n = 114 newts. 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, with μ ¯ x  and σ ¯ x to three decimal places and the others correct to two decimal places.

μ ¯ x =

σ x ¯ =

Answer 1

Solution:

Given that ,

= 216.4

= 5

A sample of size n = 114  is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 216.400

SD =      = 5/​114 = 0.468

Answer :

=  216.400

= 0.468