question 1 2 pts imagine the data on a graph has a mean ($mu = 50$) and a standard deviation ($sigma = 10$)…

Explanation:

Step1: Recall the formula for score

The formula for a score $x$ in terms of mean $\mu$ and standard - deviation $\sigma$ is $x=\mu + z\sigma$, where $z$ is the number of standard deviations from the mean.

Step2: Calculate two standard deviations above the mean

Given $\mu = 50$, $\sigma=10$, and $z = 2$. Substitute into the formula: $x=\mu+z\sigma=50 + 2\times10=50 + 20=70$.

Step3: Calculate one standard deviation below the mean

Here $z=- 1$. Substitute $\mu = 50$, $\sigma = 10$ into the formula: $x=\mu+z\sigma=50+( - 1)\times10=50 - 10 = 40$.

Step4: Calculate two standard deviations below the mean

Here $z=-2$. Substitute $\mu = 50$, $\sigma = 10$ into the formula: $x=\mu+z\sigma=50+( - 2)\times10=50-20 = 30$.

Step5: Calculate one standard deviation above the mean

Here $z = 1$. Substitute $\mu = 50$, $\sigma = 10$ into the formula: $x=\mu+z\sigma=50+1\times10=50 + 10=60$.

Answer:

Two standard deviations above the mean: 70 One standard deviation below the mean: 40 Two standard deviations below the mean: 30 One standard deviation above the mean: 60