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

karush

Well-known member
Jan 31, 2012
3,084
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
Mar 27, 2017
27
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
Jan 31, 2012
3,084
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

Screenshot 2021-09-02 11.25.39 AM.png

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:

karush

Well-known member
Jan 31, 2012
3,084

romsek

Member
Mar 27, 2017
27
\(\displaystyle \Phi^{-1}(p)\) is the inverse of \(\displaystyle \Phi(z)\)

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