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: 459

Explanation:

We can work backwards using the z-score formula to find the mean. The problem gives us the values for z, x and σ. So, let's substitute these numbers back into the formula:

z−3−54−459459=x−μσ=405−μ18=405−μ=−μ=μ

We can think of this conceptually as well. We know that the z-score is −3, which tells us that x=405 is three standard deviations to the left of the mean, and each standard deviation is 18. So three standard deviations is (−3)(18)=−54 points. So, now we know that 405 is 54 units to the left of the mean. (In other words, the mean is 54 units to the right of x=405.) So the mean is 405+54=459.

Answer 2

The mean point is 459

Explanation:

We use the formula:

`z = (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 = (405 - \mu)/( 18)`

Multiply through by 18 to get:

`- 3 * 18 = 405 - \mu`

`- 54 = 405 - \mu`

`- 54 - 405 = - \mu`

`- 459 = - \mu`

Divide through by -1

`\mu = 459`