Question

in a symmetric bell - curve, what percent of the data will be higher than one standard deviation above the mean?

Explanation:

Step1: Recall the properties of normal distribution

In a normal (bell - shaped) distribution, about 68.2% of the data lies within 1 standard deviation of the mean ($\mu\pm\sigma$). This means that the percentage of data outside of this range is $100 - 68.2=31.8\%$.

Step2: Divide the outside data

The data outside of $\mu\pm\sigma$ is split evenly between the two tails. So the percentage of data above $\mu + \sigma$ (one standard deviation above the mean) is $\frac{31.8}{2}=15.9\approx15.8\%$ (due to rounding in common approximations).

Answer:

15.8