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? 430 354 215 311

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, $\sigma$ is the standard deviation, and $z$ is the number of standard deviations from the mean. In this case, we know that $x = 3540$, $\mu=3110$, and $z = 2$ (since the score is 2 standard deviations above the mean).

Step2: Substitute the values into the formula and solve for $\sigma$

Substitute the known values into the formula $z=\frac{x - \mu}{\sigma}$:
$2=\frac{3540 - 3110}{\sigma}$
First, calculate the numerator: $3540-3110 = 430$. So the equation becomes $2=\frac{430}{\sigma}$.
To solve for $\sigma$, we can cross - multiply: $2\sigma=430$.
Then, divide both sides by 2: $\sigma=\frac{430}{2}=215$.

Answer:

215