Question

using the standard normal table find the following probabilities associated with the standard normal distribution z
p (z <2.05)
p (z>1.46)
p (1.46 <z <2.05)

Answer 1

Solution;

Given that,

a )  p (z <2.05)

Using standard normla table,
P(Z < 2.05 ) = 0.9798
To see the z value 2.00 in the column and 0.05 in the row of the standard normal table the corresponding probability is
Probability = 0.9798

b )  p (z>1.46)

= 1 - p ( z < 1.46 )

Using standard normla table,

= 1 - 0.9279

= 0.0721

Probability = 0.0721

c )  p (1.46 <z <2.05)

= p ( z < 2.05 ) - p ( z < 1.46 )

Using standard normla table,

= 0.9798 - 0.9279

= 0.0519

Probability = 0.0519