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

Explanation:

Step1: Recall the empirical rule for normal distribution

The empirical rule states that for a normal distribution:

• Approximately (68%) of the data lies within (1) standard deviation ((\mu\pm\sigma)) of the mean.
• Approximately (95%) of the data lies within (2) standard deviations ((\mu\pm2\sigma)) of the mean.
• Approximately (99.7%) of the data lies within (3) standard deviations ((\mu\pm3\sigma)) of the mean.

The area to the right of (x) is (0.16). Since the total area under the normal curve is (1), and the normal distribution is symmetric about the mean (\mu), we know that (P(X > x)=0.16) is equivalent to (P(X<\mu + z\sigma)=0.84) (because (1 - 0.16=0.84)). From the empirical rule, when (z = 1), (P(\mu-\sigma<X<\mu+\sigma)=0.68) and (P(X<\mu+\sigma)=0.5+\frac{0.68}{2}=0.84)

Step2: Calculate the value of (x)

We are given that (\mu = 71) (mean) and (\sigma=15) (standard deviation). Using the formula (x=\mu + z\sigma), with (z = 1) (from the empirical rule for the (84^{th}) percentile) (x=71+1\times15) (x = 86)

Answer:

86 minutes