Answer:
The mean point is 459
Step-by-step explanation:
We use the formula:
[tex]z = \frac{x - \mu}{ \sigma} [/tex]
Evelyn's points per pinball game are normally distributed with a standard deviation of 18 points.
This means:
[tex] \sigma = 18[/tex]
From the question, the standard deviation of 405 points is -3.
We substitute x=405, and z=-3 to get:
[tex] - 3 = \frac{405 - \mu}{ 18} [/tex]
Multiply through by 18 to get:
[tex] - 3 \times 18 = 405 - \mu[/tex]
[tex] - 54 = 405 - \mu[/tex]
[tex] - 54 - 405 = - \mu[/tex]
[tex] - 459 = - \mu[/tex]
Divide through by -1
[tex] \mu = 459[/tex]
