Question

Find the following probabilities: Please show work

a) Pr{Z < 0.33}

b) Pr{Z ≥ -0.33}
c) Pr{-1.67 < Z < 1.67}

d) Pr{-2.91 < Z < 0.0}

e) Pr{Z < -1.03 or Z > 1.03}

(you want the probability that Z is outside the range -1.03 to 1.03)

Answer 1

Solution:

Given that,

Using standard normal table

a) P ( Z < 0.33)

P ( Z < 0.33) = 0.6293

b) P ( Z -0.33 )

= 1 - P ( Z - 0.33 )

= 1 - 0.3707

= 0.6293

P ( Z -0.33 ) = 0.6293

c) P( -1.67 < Z < 1.67 )

P ( Z < 1.67 ) - P ( Z < -1.67 )

= 0.9525 - 0.0475

= 0.9050

P( -1.67 < Z < 1.67 ) = 0.9050

d) P( -2.91 < Z < 0.0)

P ( Z < 0.0) - P ( Z < -2.91 )

= 0.5000 - 0.0018

= 0.4982

P( -2.91 < Z < 0.0) = 0.4982

e) P ( Z < -1.03 or Z > 1.03)

P(Z < -1.03 )

P(Z < -1.03 ) = 0.1515

P ( Z > 1.03 )

= 1 - P ( Z < 1.03 )

= 1 - 0.8485

= 0.1515

P ( Z > 1.03 ) = 0.1515

P ( Z < -1.03 or Z > 1.03)

=  0.1515 +  0.1515

= 0.3030

P ( Z < -1.03 or Z > 1.03) = 0.3030