Question

Let Z have the standard normal distribution.

a. Find P(Z ≥ 1.21)

b. (Z < −0.52 or Z > 1.16)

c. P (0.31 ≤ Z ≤ 1.76)

.

.

Answer 1

Solution:

Given that,

a.)  P(Z ≥ 1.21)

= 1 -  P(Z ≤ 1.21)

Using standard normla table

= 1 - 0.8869

= 0.1131

Probability = 0.1131

b ) P  (Z < −0.52 or Z > 1.16)

p ( Z < - 0.52 )

Using standard normla table

= 0.3015

p (  Z > 1.16)

= 1 -  p (  Z < 1.16)

Using standard normla table

= 1 - 0.8770

= 0.1230

= 0.3015 + 0.1230

Probability = 0.4245

c ) . P (0.31 ≤ Z ≤ 1.76)

= P ( Z ≤ 1.76 ) - P ( Z ≤ 0.31 )

Using standard normla table

= 0.9608 - 0.6217

= 0.3391

Probability = 0.3391