Kth Percentile

[mkamony]

http://postimage.org/image/35ywv1jms/

Thanks ahead

[jen]

Hrm. I really don't think this is a PowerPrep question, and I think this is therefore not supposed to be posted here. Where are you getting these questions?

[mkamony]

I swear it's from Powerprep v. 1

[tommywallach]

Hey mkamony,

You kinda have to draw this to see what's going on. Basically, normal curves are shaped like a bell, so they aren't linear where the scores are concerned (that's why the answer isn't C). Instead, they get WIDER as they move outwards towards the extremes of percentage. So the section closer to the mean (from 30-45) will take up less score deviation then the section further from the mean (from 15-30), so there will be more score change closer to the mean. This means that k will actually be less than 30, because there will be more shift upwards.

You can draw it this way. Draw the two points you know (45, 550) and (15,350). Connect them with a straight line. Also connect them like a bell curve, nearing its peak (which will occur at the 50th percentile). Now, draw a line straight down from the straight connecting line, past the curvy line. Notice it doesn't hit the curvy line right in the center, but slightly to the left of center, this is where 450 is (because the scores are linear), and the percentile is to the left of the halfway point on the curvy line (hence to the left of 30).

Make sense?

-t