Question

How do you find the z-score for which 98% of the distribution's area lies between -z and z?

Answer 1

`z=2.33`

Explanation:

You need to look this up from a z-score table (e.g. http://www.had2know.com/academics/normal-distribution-table-z-scores.html) or use a numerical implementation of the inverse normal distribution cumulative density function (e.g. normsinv in Excel). Since you desire the 98% percent interval you desire 1% on each side of `+-z`, look up 99% (0.99) for `z` to obtain this.

The closest value for 0.99 on the table gives `z=2.32` on the table (2.33 in Excel), this is your `z` score.