Question

For a standard normal distribution, determine the probabilities of obtaining the following z values. It is helpful to draw a normal distribution for each case and show the corresponding area.

(a)

greater than zero

(b)

between −2.0 and −1.5

(c)

less than 1.5

(d)

between −1.2 and 1.2

(e)

between 1.35 and 1.85

Answer 1

Solution

Using standard normal table

a ) P ( Z < - 0.64 )

= 0.2611

Probability = 0.2611

b ) P ( Z > 0 )

1 - P ( Z < 0)

= 1 - 0.5000

= 0.5000

Probability = 0.5000

b ) P ( −2.0 < Z < -1.5 )

P ( Z < -1.5 ) - P ( Z < −2.0)

= 0.0668 - 0.0228

= 0.0440

Probability = 0.0440

c ) P ( Z < 1.5 )

= 0.9332

Probability = 0.9332

d ) P ( −1.2 < Z < 1.2 )

P ( Z < 1.2 ) - P ( Z < −1.2 )

= 0.8849 - 0.1151

= 0.7698

Probability = 0.7698

e ) P ( 1.35 < Z < 1.85 )

P ( Z < 1.85 ) - P ( Z < 1.35 )

= 0.9678 - 0.9115

= 0.0563

Probability = 0.0563