Question

Find the following probabilities for the standard normal random variable Z:

(Give answers to four decimal places.)

a) P(Z ≤ 2.1)  

b) P(Z ≥ 2.1)  

c) P(Z ≥ -1.65)

d) P(-2.13 ≤ Z ≤ -.41)

e) P(-1.45≤ Z ≤ 2.15)

f) P(Z ≤ -1.43)

Answer 1

Solution :

Given that,  

Using standard normal table ,

a)

P(z 2.1) = 0.9821

b)

P(z 2.1) = 1 - P(z 2.1) = 1 - 0.9821 = 0.0179

c)

P(z -1.65) = 1 - P(z -1.65) = 1 - 0.0495 = 0.9505

d)

P(-2.13 z -.41)

= P(z -.41) - P(z -2.13)

= 0.3409 - 0.0166

= 0.3243

P(-2.13 z -.41) = 0.3243

e)

P(-1.45 z 2.15)

= P(z 2.15) - P(z -1.45)

= 0.9842 - 0.0735

= 0.9107

P(-1.45 z 2.15) = 0.9107

f)

P(z -1.43) = 0.0764