use the empirical rule to find a reasonable estimate for p(z ≤ 0.82). 10% 30% 50% 80% done standard normal…

Answer:

D. 80%

Explanation:

Step1: Recall empirical - rule basics

The empirical rule for a standard normal distribution 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 mean of a standard normal distribution is $z = 0$ and the total area under the curve is 1 or 100%.

Step2: Analyze the position of $z = 0.82$

The area to the left of $z = 0$ is 50% (since the standard normal distribution is symmetric about $z = 0$). The value $z=0.82$ is close to $z = 1$. The area between $z = 0$ and $z = 1$ is approximately $\frac{68%}{2}=34%$.

Step3: Calculate the area to the left of $z = 0.82$

$P(z\leq0.82)\approx50% + \text{(area between }z = 0\text{ and }z = 0.82)$. Since $z = 0.82$ is close to $z = 1$, the area between $z = 0$ and $z = 0.82$ is close to 30%. So $P(z\leq0.82)\approx50%+30% = 80%$.