Raymond B. answered 09/29/20
Math, microeconomics or criminal justice
z score for the mean with 50% of the observations below is zero
The empirical rule 84-95-99.7 has a z score of 2 for 95% of the observations falling within 2 standard deviations from the mean, that's the same as 97.5% below that z score, as the 100-95% gets split in two, above z=2 and below z=-2
For 5% below, that's a little more than z=-2, maybe z=-1.9 You need to look at a z score table.
A z-score of +2 has 2.5% above it. For 5% above, it's a little less than z=2, maybe 1.9
You can find z score tables on line, or with a statistics calculator, which is also online
z=-1.645 has 95% of the observations above it and 5% below, approximately