Question

Determine the value z* that satisfies the conditions below. (Round all answers to two decimal places.)

(a) Separates the largest 3.2% of all z values from the others
z* =  

(b) Separates the largest 0.8% of all z values from the others
z* =  

(c) Separates the smallest 5.6% of all z values from the others
z* =

(d) Separates the smallest 12.1% of all z values from the others
z* =

Answer 1

Solution :-

a)

The ' z ' Ditribution of the largest 3.2 % is ,

P ( Z > z ) = 3.2 %

1 - P ( Z < z ) = 0.032

P ( Z < z ) = 1 - 0.032

P ( Z < z ) = 0.968

By using standard normal ( z ) table,

P ( Z < 1.852 ) = 0.968

z = 1.85

------------------------------

b)

The ' z ' Ditribution of the largest 0.8 % is ,

P ( Z > z ) = 0.8 %

1 - P ( Z < z ) = 0.008

P ( Z < z ) = 1 - 0.008

P ( Z < z ) = 0.992

By using standard normal ( z ) table,

P ( Z < 2.409 ) = 0.992

z = 2.41

------------------------------

c)

The ' z ' Ditribution of the Smallest 5.6 % is ,

P ( Z < z ) = 5.6 %

P ( Z < z ) = 0.056

By using standard normal ( z ) table,

P ( Z < - 1.589 ) = 0.056

z = - 1.59

---------------------------------

d)

The ' z ' Ditribution of the Smallest 12.1 % is ,

P ( Z < z ) = 12.1 %

P ( Z < z ) = 0.121

By using standard normal ( z ) table,

P ( Z < - 1.17 ) = 0.121

z = - 1.17