# Math Help - Standard normal R.V. question

1. ## Standard normal R.V. question

Let Z be the standard normal random variable. If z>0 and P(Z<=z) = a , what are P[Z<=(-z)] and P(-z<Z<z) ?

<= is supposed to mean less than or equal to, I just didn't know how to type that

I know that the answers are 1-a, and 2a-1. I just can't figure out how to show this.

2. Originally Posted by babbagandu
Let Z be the standard normal random variable. If z>0 and P(Z<=z) = a , what are P[Z<=(-z)] and P(-z<Z<z) ?

<= is supposed to mean less than or equal to, I just didn't know how to type that

I know that the answers are 1-a, and 2a-1. I just can't figure out how to show this.
Draw pictures!!

By symmetry, $\Pr(Z \leq -z) = \Pr(Z \geq z) = 1 - a$.

$\Pr(-z \leq Z \leq z) = 1 - \Pr(Z \leq -z) - \Pr(Z \geq z)$.