How do I calculate mu and sigma?

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Suppose that $X \sim N(\mu, \sigma^2)$ and that ${P(X \le 5) = 0.8}$ and $P(X\ge 0) = 0.6$ What are the values of $\mu$ and $\sigma^2$

So far I've calculated $\frac{5-\mu}{ \sigma} = 0.84$ now I don't know where I would go from this point to calculate $\mu$

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1 Answer

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Guide:

From $$P(X \geq 0 ) = 0.6$$

we have

$$P\left(\frac{X-\mu}{\sigma} \geq \frac{0-\mu}{\sigma} \right) = 0.6$$

You should be able to obtain another linear equation from above.

With two equations and two unknown, you should be able to solve for your $\mu$ and $\sigma$.

Edit:

If you have $$\frac{5-\mu}{\sigma}=0.84$$ then we can write them as $$5=\mu+0.84\sigma\tag{1}$$

If we have $$\frac{0-\mu}{\sigma}=c$$

where $c$ is a known value.

then we have $$0=\mu+c\sigma\tag{2}$$

Hence, we just have to solve $(1)$ and $(2)$ simultaneously for example by elimination or substitution.

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