Question

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? 215 354 430 311

Explanation:

Step1: Set up the formula

Let $\mu$ be the mean, $\sigma$ be the standard - deviation, and $x$ be the score. The formula for the $z$ - score is $z=\frac{x - \mu}{\sigma}$. We know that $x = 3540$, $\mu=3110$, and $z = 2$.

Step2: Substitute values into formula

Substitute the known values into $z=\frac{x - \mu}{\sigma}$, we get $2=\frac{3540 - 3110}{\sigma}$.

Step3: Solve for $\sigma$

First, simplify the numerator: $3540−3110 = 430$. So the equation becomes $2=\frac{430}{\sigma}$. Cross - multiply to get $2\sigma=430$. Then divide both sides by 2: $\sigma=\frac{430}{2}=215$.

Answer:

215