if income in the us was normally distributed, what z-score would represent the top 1%?
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the Z score that would correspond to that proportion.
- Forwarded message -From: Debbie Tomasovic Date: Sat, May 26, 2012 at 10:07 AMSubject: DV rerasechTo: Marna,Below are two emails from Eric Mankowski, Ph.D. with PSU regarding his interpretations of some of the recent DV effectiveness rerasech. He will be one of our keynote speakers at the August NW Association of Domestic Violence Treatment Providers in Vancouver. Thank you for being open to receiving this input.Debbie Tomasovic, LMFTA Better Way CounselingDomestic Violence Treatment ProviderVancouver, WashingtonDebbie,I have been out of town and away from email, so sorry for the delayed response. Yes, you can forward my email. It's important also to note, which I did not below, that Gondolf's finding of the 50% reduction in re-assault among program attenders held even after statistically controlling for demographic characteristics, and personality and behavioral differences among the attenders vs. drop outs. The reduction in re-assault cannot be explained by demographic differences in those who attend vs. drop out.Finally, please note that I mistakenly wrote below about the California study as showing promising outcomes in Oregon , which should have been California .-EricOn Thu, May 17, 2012 at 9:56 AM, Debbie Tomasovic wrote:I appreciate your thoughtful response. May I forward this and or your follow up email on Monday to Marna Miller? Debbie Tomasovic
To find the z-score that represents the top 1% of incomes in the US, we need to use the properties of the normal distribution.
Step 1: Determine the area under the normal curve corresponding to the top 1%.
In this case, we are interested in the area to the right of this percentile since we want to find the z-score for the top 1%. The remaining area to the left of this percentile represents the bottom 99% of incomes.
Step 2: Use a standard normal distribution table or calculator.
Since the standard normal distribution has a mean of 0 and a standard deviation of 1, we can use a standard normal distribution table or calculator to find the corresponding z-score.
Step 3: Find the z-score.
Look up the area corresponding to the top 1% in the standard normal distribution table. This area is typically listed under the column labeled "Probability" or directly under the curve in some calculators. Once you find the area, locate the corresponding z-score in the column labeled "Z-Score."
The standard normal distribution table typically provides values for the area to the left of a given z-score. To find the z-score corresponding to the top 1%, subtract the area from 1.
For example, if the area to the left of the top 1% is 0.99, then the area to the right (representing the top 1%) is 1 - 0.99 = 0.01. We can locate the z-score corresponding to this area in the standard normal distribution table.
Remember that the z-score is a measure of how many standard deviations an observation is away from the mean. So, a positive z-score for the top 1% means that the income is above the mean.
Using this approach, you can find the z-score that represents the top 1% of incomes in the US population.