Question

Evelyn's points per pinball game are normally distributed with a standard deviation of 18 points. If Evelyn scores 405 points, and the z-score of this value is −3, then what is her mean points in a game?

Answer 1

Answer:

The mean point is 459

Step-by-step explanation:

We use the formula:

$z = \frac{x - \mu}{ \sigma}$

Evelyn's points per pinball game are normally distributed with a standard deviation of 18 points.

This means:

$\sigma = 18$

From the question, the standard deviation of 405 points is -3.

We substitute x=405, and z=-3 to get:

$- 3 = \frac{405 - \mu}{ 18}$

Multiply through by 18 to get:

$- 3 \times 18 = 405 - \mu$

$- 54 = 405 - \mu$

$- 54 - 405 = - \mu$

$- 459 = - \mu$

Divide through by -1

$\mu = 459$