Question

Find a z value to the left of the mean so that 92.9% of the distribution lies to the right of it.

Answer 1

Using the chart at this link
http://www.mathsisfun.com/data/standard-normal-distribution-table.html
look inside the chart for the area .429 or the closest value to it. .4292 is closest and reads out to a z score of -1.47.
Note: 92.9 - 50 = 42.9. Half the area lies to the right of the mean.
Then, .4292 of the area lies between z = -1.47 and the mean which is z = 0.
So from z = -1.47 all the way to the right tail of the curve is 92.9% of the area under the curve.