Given the area to the right of a z value is 05672 find the z

Given the area to the right of a z value is 0.5672, find the z value SHOW WORK!!!

Solution

I am assuming you have a z table to work with? Most z-tables are cumulative, meaning that they give you areas to the left of a z value. However, you want the area to the right of a value to be 10%, or .1. So, if we are looking inside the table (where the areas are... numbers that are likely four digits beyond a decimal place), we are looking for the number closest to 1-.1 (since the area under the entire curve is 1, and we want the area to the RIGHT to be .1) = .9. The number closest to .9 in the table is .8997, meaning the z value associated with it (if we trace back to the horizontal and vertical values of the table that yield .8997) is 1.28. Does this make sense? You could further show work by actually drawing a normal curve to show where this number is (to the right of the middle quite a ways) and shading the 10% area to the right of the number 1.28.