Find a $z$ value to the right of the mean so that $84.1 \%$ of the distribution lies to the left of it. Refer to the table of values Area Under the Standard Normal Distribution as needed. \[ z= \]

Step 1 ：Find a z-value to the right of the mean so that 84.1\% of the distribution lies to the left of it. Refer to the table of values Area Under the Standard Normal Distribution as needed.

Step 2 ：\[z=\]

Step 3 ：Using a standard normal distribution table or a calculator, we find the z-value corresponding to an area of 0.841.

Step 4 ：\[z \approx 0.9986\]

Step 5 ：\(\boxed{z \approx 0.9986}\)