Finding a value in a normal distribution given the probability

Question

I have a normal distribution and the only value I am given is the mean, which is 3. For a certain value of a, I have p(X>a) = 16%. This curve is simetrical to the equation x = 3

How do I find a?

I apologize if information is missing, this is from my maths schoolbook and that sort of mistakes happens. I copied the problem as it is.

Thanks.

Answer 1

If $\Phi(x)$ if the cumulative density function of a standard normal distribution (with mean $0$ and variance $1$) then $\Phi^{-1}(1-0.16)\approx 0.9944579$ so $\frac{a-\mu}{\sigma}\approx 0.9944579$ and thus $$a \approx \mu + 0.9944579\sigma$$

You know $\mu=3$. To find $a$ you need $\sigma$.

Alternatively, to find $\sigma$, you need $a$.