Question

question 1
imagine the data on a graph has a mean (μ = 50) and a standard deviation (σ = 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 calculation

Score = $\mu\pm n\sigma$, where $\mu$ is the mean, $n$ is the number of standard - deviations, and $\sigma$ is the standard deviation.

Step2: Calculate score two standard deviations above the mean

Score = $\mu + 2\sigma$. Substitute $\mu = 50$ and $\sigma = 10$. So, Score = $50+2\times10=70$.

Step3: Calculate score one standard deviation below the mean

Score = $\mu-\sigma$. Substitute $\mu = 50$ and $\sigma = 10$. So, Score = $50 - 10=40$.

Step4: Calculate score two standard deviations below the mean

Score = $\mu - 2\sigma$. Substitute $\mu = 50$ and $\sigma = 10$. So, Score = $50-2\times10 = 30$.

Step5: Calculate score one standard deviation above the mean

Score = $\mu+\sigma$. Substitute $\mu = 50$ and $\sigma = 10$. So, Score = $50 + 10=60$.

Answer:

Score that is two standard deviations above the mean: 70
Score that is one standard deviation below the mean: 40
Score that is two standard deviations below the mean: 30
Score that is one standard deviation above the mean: 60