# Finding the Mean for Normal Distribution

I'm a little stuck trying to find the mean of this practice normal distribution question.

Standard deviation $$= 300$$

$$20$$% of workers are paid less than $$1500$$

So I created the probability like this

$$P(x < 1500) = 0.2$$

But I'm unsure what I'm meant to do next

Any help is appreciated!

Go back to the standard normal distribution, with mean $$0$$ and $$\sigma=1$$. If $$X$$ is normally distributed, $$\frac{X-\mu}{\sigma}$$ is standard-normally distributed and for $$\Phi$$ (the cdf for the SND) tables exist.
From this table I get that $$\Phi(-0.84) \approx 0.2005$$ which is a nice approximation to $$0.2$$. Many calculators can compute $$\Phi^{-1}$$ as well, nowadays (in my old high school days we had to do it with tables though).
So we know that when $$\frac{1500-\mu}{300}$$ should be about $$-0.84$$ to get the correct probability. Now compute $$\mu$$.