Standard normal RV probability

Question

Z is a standard normal random variable

I need to find $P(|Z|<.95)$, find c such that $P(|Z|<c)$, and given that X is a RV with mean 3 and standard deviation 16, find $P(X>3.84)$

I am just confused by the absolute value bars, what do I do with those?

Answer 1

The notation $|x|$ means, "$x$ or $-x$, whichever is greater." For your purposes, what you really need to know is that $|Z| < c$ is the same as writing $-c < Z < c$.

It is perhaps also useful to know that if $Z$ is a standard normal random variable (expected value zero), then $P(Z<-c) = P(Z>c)$, and therefore $P(|Z|<c) = 1 - 2 P(Z > c)$. In other words, if you cut off the tails of the distribution at equal distances from the middle, so that $5$% of the distribution is in each tail, you will have $10$% of the distribution in the two tails together.