Question

For a population with m = 60, which of the following values for the population standard deviation would cause X = 68 to have the most extreme position in the distribution?A. s=4B. s=3C. s=2D. s=1

Answer 1

Option D) s = 1

Explanation:

We are given the following information in the question:

Mean, μ = 69

X = 68

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

Computing z-scores for different standard deviation:

`z_1 = \displaystyle(68-60)/(4) = 2\\\\z_2 = \displaystyle(68-60)/(3) = 2.667\\\\z_3= \displaystyle(68-60)/(2) = 4\\\\z_4 = \displaystyle(68-60)/(1) = 8`

The standard deviation with highest z-score gives the most extreme position in the distribution.

Thus, the most extreme position of X = 68 in the distribution is given by a standard deviation of 1.

Option D) s = 1