solve the problem. 9) for a standard normal distribution, find the percentage of data that are between 2…

Explanation:

Step1: Recall z - scores

In a standard normal distribution, the z - score represents the number of standard deviations from the mean. A value 2 standard deviations below the mean has a z - score of $z_1=- 2$ and a value 1 standard deviation above the mean has a z - score of $z_2 = 1$.

Step2: Use the standard normal table

The standard normal table gives the cumulative probability $P(Z\leq z)$. From the standard - normal table, $P(Z\leq - 2)=0.0228$ and $P(Z\leq1)=0.8413$.

Step3: Calculate the probability between the two z - scores

The probability $P(-2<Z<1)$ is given by $P(Z < 1)-P(Z < - 2)$. So, $P(-2<Z<1)=0.8413 - 0.0228=0.8185$.

Answer:

81.85%