# 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?

Aug 24, 2017

$- 0.71$

#### Explanation:

For $Z \text{ "~" } N \left(0 , 1\right)$

we require

$P \left(Z > z\right) = 0.76$

Two things need to be remembered:

1. Tables usually give the values for $P \left(Z < z\right)$

2. $P \left(Z < 0\right) = 0.5$

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

Because $P \left(Z > - z\right) = P \left(Z < z\right)$.

i.e. to find $P \left(Z > z\right) = 0.76$, find $P \left(Z < z\right) = 0.76$ instead, by table lookup

which gives $z = 0.71$ to 2 decimal places

so

P(Z>z)=0.76" "=>" "z=–0.71