the graph shows the distribution of the number of text messages young adults send per day. the distribution…

Answer:

A. 16%

Explanation:

Step1: Calculate z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 158$, $\mu=128$, $\sigma = 30$. So $z=\frac{158 - 128}{30}=\frac{30}{30}=1$.

Step2: Use the empirical rule

For a normal distribution, about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), which means 34% of the data lies between $\mu$ and $\mu+\sigma$ and 34% lies between $\mu$ and $\mu - \sigma$. The total area to the left of $\mu+\sigma$ is 50%+34% = 84%. So the area to the right of $\mu+\sigma$ (i.e., the percentage of values greater than $\mu+\sigma$) is 100% - 84%=16%. Since $x = 158=\mu+\sigma$ (with $\mu = 128$ and $\sigma = 30$), the percentage of young adults who send more than 158 text messages per day is 16%.