The mean of a normally distributed data set is 75 with a standard deviation of 5 . Find the data value that is greater than $8\mathrm{\%}$ of the data.
Click here to see page 1 of the table for areas under the standard normal curve.
Click here to see page 2 of the table for areas under the standard normal curve.

The data value that is greater than $8\mathrm{\%}$ of the data is $◻$.
(Round to the nearest whole number as needed.)

Step 1 ：Find the z-score that corresponds to the 8% percentile. Since the problem asks for the data value that is greater than 8% of the data, we need to look at the lower tail of the distribution.

Step 2 ：Use a standard normal distribution table to find the z-score that corresponds to the 8% percentile. The z-score is approximately -1.41.

Step 3 ：Use the z-score formula to find the corresponding data value. The z-score formula is $Z=\frac{X-\mu }{\sigma }$, where Z is the z-score, X is the data value, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step 4 ：Rearrange the formula to solve for X: $X=Z\sigma +\mu$.

Step 5 ：Substitute the values into the formula: $X=-1.41\ast 5+75$.

Step 6 ：Calculate the above expression: $X=-7.05+75$.

Step 7 ：Round to the nearest whole number: $X=68$.

Step 8 ：$\boxed{{\displaystyle 68}}$ is the data value that is greater than 8% of the data.