Question

2. a) Find the area under the standard normal curve to the right of z = 1.5.

b) Find the area under the standard normal curve to the left of z = 1.

c) Find the area under the standard normal curve to the left of z = -1.25.

d) Find the area under the standard normal curve between z = -1 and z = 2.

e) Find the area under the standard normal curve between z = -1.5 and z = 1.5.

f) Find the sum of the areas under the standard normal curve to the left of z = -1.5 and to the right of z = 1.5

Answer 1

Solution

Using standard normal table

a ) P ( Z > 1.5 )

1 - P ( Z <  1.5 )

= 1 - 0.9332

= 0.0668

The area = 0.0668

b ) P ( Z < 1 )

=0.8413

The area = 0.8413

c ) P ( Z < -1.25 )

=0.1056

The area = 0.1056

d ) P ( - 1 < Z < 2)

P ( Z < 2 ) - P ( Z < -1 )

= 0.9772 - 0.1587

= 0.8185

The area = .8185

d ) P ( - 1.5 < Z < 1.5 )

P ( Z < 1.5 ) - P ( Z < -1.5 )

= 0.9332 - 0.0668

= 0.8664

The area = 0.8664

e ) P ( Z < -1.5 )

=0.0668

P ( Z > 1.5 )

1 - P ( Z <  1.5 )

= 1 - 0.9332

= 0.0668

The area = 0.0668 + 0.0668 = 0.1336