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 $\mu$.


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