1. ## Normal Distribution

I know how to find out the probability within a given range on the normal distribution curve, but a textbook suddenly asked about finding the mean.

There's an unknown mean and a standard deviation of 0.6. I have to calculate the mean if the values after 5.7 have a probability of 0.14.

The answer is obviously provided in the textbook, but that's all there is. A step-by-step procedure would be awesome. Thanks in advance.

2. Originally Posted by Lupin
I know how to find out the probability within a given range on the normal distribution curve, but a textbook suddenly asked about finding the mean.

There's an unknown mean and a standard deviation of 0.6. I have to calculate the mean if the values after 5.7 have a probability of 0.14.

The answer is obviously provided in the textbook, but that's all there is. A step-by-step procedure would be awesome. Thanks in advance.
Pr(X > 5.7) = 0.14.

Find the value z* of Z such that Pr(Z > z*) = 0.14.

From $\displaystyle Z = \frac{X - \mu}{\sigma}$ it follows that:

$\displaystyle z* = \frac{5.7 - \mu}{0.6}$.

Substitute your value of z* and solve for $\displaystyle \mu$.