#A study of hedge fund investors found that their annual household incomes are normally distributed with a mean of $175,000 and a standard deviation of $25,000. The percentage of hedge fund investors that have incomes greater than $225,000 is closest to ?
I’m using this formula [z = (observation - Mean) / standard deviation] and I’m getting 2. How to see this in z table and which table should I use as there are two different tables.
Please help me in understanding this question.
Thanks!
You should use a table that has a title like “cumulative z-table, for z >= 0”. I only have Schweser Notes in front of me right now but there you can find that table in the Appendix of the quantitative methods book. You then find the entry that corresponds to 2.00 (the schweser table actually has rows denote steps of 0.1 width and the columns then denoting 0.01 steps starting from the row number, so you find the row that says “2.0” and the column that says “0.00”. the corresponding entry is what you are after). This entry should read 0.9772 and is the probability that you will find an z-score equal to or lower to 2.00. That is the probability to find an income equal to or lower than $225.000. So in order to find the probability of having an income above that threshold you do 1 - 0.9772 = 0.0228 = 2.28 %.
Aside: As this is exactly 2 standard deviations away from the mean it might be helpful to know this number “by heart”. A normal distribution has roughly 95% of values within 2 standard deviations of the mean and thus roughly 2.5% of results above 2 standard deviations above the mean. Knowing this would enable you to solve such a question within seconds on the actual exam.
Thank you!