priya is playing a game where she earns online badges for scoring higher than the mean score on a level…

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 with $z=\frac{x - \mu}{\sigma}$, 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 the formula $\sigma=\frac{x - \mu}{z}$. We have $\sigma=\frac{3540 - 3110}{2}$.

Step4: Calculate the value of $\sigma$

First, calculate the numerator: $3540−3110 = 430$. Then, divide by $z$: $\frac{430}{2}=215$.

Answer:

215