# [SOLVED]7.6.69 Determine the value z^* that..

#### karush

##### Well-known member
Determine the value $z^*$ that...
a. Separates the largest $3\%$ of all z values from the others
$=1.88$
b. Separates the largest $1\%$ of all z values from the others
$=2.33$
c. Separates the smallest $4\%$ of all z values from the others
$=1.75$
d. Separates the smallest $10\%$ of all z values from the others
$=1.28$

OK just can't seem to find an example of how these are stepped thru
the book answer follows the =

#### romsek

##### Member
once again $$\displaystyle \Phi(z)$$ is the CDF of the standard normal distribution
you'll need some way to compute the inverse of this function to complete this problem.

a)$$\displaystyle \Phi(z^*) = 0.97\\ z^* = \Phi^{-1}(0.97)= 1.88079$$

b) $$\displaystyle \Phi(z^*) = 0.99$$

c) $$\displaystyle \Phi(z^*) = 0.04$$

d)$$\displaystyle \Phi(z^*) = 0.1$$

#### karush

##### Well-known member
once again $$\displaystyle \Phi(z)$$ is the CDF of the standard normal distribution
you'll need some way to compute the inverse of this function to complete this problem.

a)$$\displaystyle \Phi(z^*) = 0.97\\ z^* = \Phi^{-1}(0.97)= 1.88079$$

b) $$\displaystyle \Phi(z^*) = 0.99$$

c) $$\displaystyle \Phi(z^*) = 0.04$$

d)$$\displaystyle \Phi(z^*) = 0.1$$
mahalo I was unaware of the use of that symbol

ok I can see that at 1.88 goes to .97 on table
or using P to z calculator but still what is $\Phi^{-1}$

Last edited:

#### romsek

##### Member
$$\displaystyle \Phi^{-1}(p)$$ is the inverse of $$\displaystyle \Phi(z)$$

If you are given a probability $$\displaystyle p, \Phi^{-1}(p)$$ returns the associated z-score of $$\displaystyle p$$