Question

Unlike scientists or statisticians, economists often break the range of a random variable into five parts, or quintiles. For a standard normal distribution, what is the z-score that defines the second quintile, the 40% point? (a) 0.40 (b) -0.40 (c) 0.253 (d) -0.253 (e) -0.842

Answer 1

(d) -0.253

Explanation:

According to a z-score table for a standard normal distribution, a z-score of -0.25 corresponds to the 40.13th percentile, and a z-score of -0.26 corresponds to the 39.74th percentile.

Interpolating those values gives us the z-score for the 40th percentile. The 40.13th percentile is twice as close to the 40th percentile than the 39.74th, thus:

`z = -0.25*(2)/(3)-0.26*(1)/(3) \\z=-0.253`

The answer is (d) -0.253.