I can't figure out at all how to do this problem. Any notes I have found on the topic have been really vague. Any help would be appreciated!
Let X be a normal random variable with mean 12 and variance 4.
Find approximations to the following:
(a) the value of a such that P(X > a) = 0.10.
(b) the value of b such that P(X < b) = 0.05.
(c) the value of c such that P(−c < X − 12 < c) = 0.95.
(d) the value of d such that P(12 − d < X < 12 + d) = 0.3
You should have a look at the standard normal table (https://en.wikipedia.org/wiki/Standard_normal_table).
$X$ is a normal random variable with mean $12$ and variance $2^2$, meaning that
$$Z=\frac{X-\mu}{\sigma} = \frac{X-12}{2}$$
is a normal random variable with mean $0$ and variance $1$. The probabilities you are interested in can then be found in tables such the ones above.