Question

Find the value z of a standard normal variable Z that satisfies each of the following conditions. In each case, sketch a standard normal curve with your value of z marked on the axis. (Do this on paper. Your instructor may ask you to turn in this work.)

(a) 5% of the observations fall below z.
z =

(b) 25% of the observations fall above z.
z =

Answer 1

a) z = -1.645

b) z = 0.674

Explanation:

We have to find the value of z of a standard normal variable Z that satisfies each of the following conditions.

a) 5% of the observations fall below z

`=P(Z < z) = 0.05`

Calculation the value from standard normal z table, we have,

`P(Z<-1.645) = 0.05\\z = -1.645`

b) 25% of the observations fall above z

`P(Z > z) = 0.25\\\Rightarrow P(Z<z) = 1 - P(Z>z) = 1 - 0.25 = 0.75`

Calculation the value from standard normal z table, we have,

`P(Z<0.674) = 0.75\\z = 0.674`