Question

question 1 2 pts imagine the data on a graph has a mean ($mu = 50$) and a standard deviation ($sigma = 10$). what would be the score that is two standard deviations above the mean? select what would be the score that is one standard deviation below the mean? select what would be the score that is two standard deviations below the mean? select what would be the score that is one standard deviation above the mean? select

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