Question

Please compute the following:
a) P(Z > 1.26), . P(Z < −0.86), P(Z > −1.37), P(−1.25 < Z < 0.37), . P(Z ≤ −4.6)
b) Find the value ? such that ?(? > ?) = 0.05
c) Find the value of ? such that ?(−? < ? < ?) = 0.99

Answer 1

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you

We make use of the Z tables wherever possible to convert Z to cumulative probabilty or vice-versa.

All answers are rounded to 4 decimal places. All answers are highligted in bold.

a) .

i) P(Z > 1.26)

= 1 - P(Z < 1.26)

= 1- 0.8962

= 0.1038

ii) P(Z < −0.86),

= 0.1949

iii) P(Z > −1.37)

= 1 - P(Z < -1.37)

= 1 - 0.0853

= 0.9147

iv)

P(−1.25 < Z < 0.37) =

= P(Z<.37) - P(Z<-1.25)

= .6443 - .1056

= 0.5387

v)

P(Z ≤ −4.6)

= 0.0000

b) Find the value ? such that ?(? > ?) = 0.05

P(Z>z) = 1-P(Z<z) = .05

P(Z<z) = .95

z = 1.6449

c)

Find the value of ? such that ?(−? < ? < ?) = 0.99

This can be expressed as :

2*P(-z<Z) = 1-.99

P(-z<Z) =(1- .99)/2 = (.01)/2 = .005

-z = -2.5758 or

z = 2.5758