the graph shows the distribution of the amount of time (in minutes) people spend watching tv shows on a…

Answer:

C. 86 minutes

Explanation:

Step1: Recall the properties of normal distribution

In a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean ($\mu\pm\sigma$), about 95% lies within 2 standard deviations ($\mu\pm2\sigma$), and about 99.7% lies within 3 standard deviations ($\mu\pm3\sigma$). If 16% of people spend more than a certain amount of time, then 84% of people spend less than that amount. Looking at the standard normal distribution table (or using the empirical rule), the z - score corresponding to a cumulative probability of 0.84 is approximately $z = 1$.

Step2: Use the z - score formula

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value from the data set, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know that $z = 1$, $\mu=71$ minutes, and $\sigma = 15$ minutes. Rearranging the formula for $x$ gives $x=\mu+z\sigma$.

Step3: Calculate the value of $x$

Substitute $\mu = 71$, $z = 1$, and $\sigma=15$ into the formula $x=\mu + z\sigma$. So $x=71+1\times15=86$ minutes.