-7.6.69 Determine the value z^* that...

[karush]

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]

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]

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 $\Phi^{-1}$

 

[karush]

Overleaf PDF statistics with MHB replies
Im hoping to get this up to 100+ pages
Mahalo much for so much valuable input

 

[romsek]

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

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

 

[HOI]

Since \(\displaystyle \Phi(1.88)= 0.97\), \(\displaystyle \Phi^{-1}(0.97)= 1.88\)