Question 476009

I believe your question is to find a range going from the mean to a {{{z-value}}} on the standard normal distribution that corresponds to {{{17}}}% of the area. A normal distribution goes from values of minus infinity to positive infinity. A standard normal distribution has a {{{mean}}} of {{{0}}} and an {{{standard}}} {{{deviation}}} of {{{1}}}.

It is usually best if you draw a diagram, in this case a bell shape curve with {{{mean = 0}}}. The area to the left of the mean is {{{50}}}% of the total area. We find a z value that corresponds to {{{67}}}% (50% + 17%) of the area to the left of this value. This can be done either with a lookup table or a spreadsheet program. I prefer excel, +{{{norminv(0.67) = 0.44}}}.

The problem could also be worded to find the area going from a z-value to the mean. In this case, we must find a z-value that corresponds to {{{33}}}% (50%-17%). Using Excel, I calculate +{{{norminv(0.33) = -0.44}}}.