Thread: 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.

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, .

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