use the empirical rule to find a reasonable estimate for p(z ≤ 0.82).\n10%\n30%\n50%\n80%\ndone

Explanation:

Step1: Recall empirical rule basics

The standard normal distribution has mean 0 and standard - deviation 1. The empirical rule states that about 68% of the data lies within 1 standard - deviation of the mean ($z=-1$ to $z = 1$), about 95% lies within 2 standard - deviations ($z=-2$ to $z = 2$), and about 99.7% lies within 3 standard - deviations ($z=-3$ to $z = 3$). The total area under the curve is 1 or 100%. The area to the left of $z = 0$ is 50%.

Step2: Analyze $z = 0.82$ position

Since $z=0.82$ is between $z = 0$ and $z = 1$. The area between $z = 0$ and $z = 1$ is approximately $\frac{68%}{2}=34%$. The area to the left of $z = 0$ is 50%. So, $P(z\leq0.82)\approx50% + \frac{68%}{2}$.

Step3: Calculate the probability

$P(z\leq0.82)\approx50%+34% = 84%$, which is closest to 80%.

Answer:

80%