priya is playing a game where she earns online badges for scoring higher than the mean score on a level…
priya is playing a game where she earns online badges for scoring higher than the mean score on a level. after the tenth level, she scores 3,540 points, which is 2 standard deviations above the mean score of 3,110 points. what is the standard deviation of scores for the tenth level? 215 311 354 430
Answer
Explanation:
Step1: Recall the z - score formula
The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation. We know that $x = 3540$, $\mu=3110$, and $z = 2$.
Step2: Rearrange the z - score formula to solve for $\sigma$
Starting from $z=\frac{x - \mu}{\sigma}$, we can cross - multiply to get $z\sigma=x - \mu$. Then, $\sigma=\frac{x - \mu}{z}$.
Step3: Substitute the given values into the formula
Substitute $x = 3540$, $\mu = 3110$, and $z = 2$ into $\sigma=\frac{x - \mu}{z}$. So, $\sigma=\frac{3540 - 3110}{2}=\frac{430}{2}=215$.
Answer:
215