Question

For a normal distribution, what z-score value separtes the lowest 20% of the distribution from the highest 80%?

Answer 1

assuming mean=0 and sd = 1; you want to find the z-score that corresponds to the first 20% of the graph. The z-score is found in my "z-table" by subtracting 20% from 50% to obtain the distance away from the mean value. When I look at the z-table in the back of the book, I want to find a number in the middle of the table that is closest to ".3000" (50% - 20% = 30%) The closest value I find in the field is: .2995. I follow this out to the left (.8) and up to the top (.04) to get the numbers for the z-score: left+top. z-score = .84 This has to be evaluated for its placement. If the z-score is to the left of the mean; we negate it; if its to the right of the mean, we keep it a positive value. 20% is less than 50% so its to the left of our mean: z-score = -.84