Question

What is the the value of z for which the area under the normal curve to the right of z is equal to 0.76?

0.33?

Answer 1

`-0.71`

Explanation:

For `Z" "~" "N(0,1)`

we require

`P(Z>z)=0.76`

Two things need to be remembered:

1. Tables usually give the values for `P(Z < z)`

2. `P(Z < 0)=0.5`

So the `z` value in this case will be negative `z`

Because `P(Z> -z)=P(Z< z)`.

i.e. to find `P(Z>z)=0.76`, find `P(Z < z) = 0.76` instead, by table lookup

which gives `z=0.71` to 2 decimal places

so

`P(Z>z)=0.76" "=>" "z=–0.71`