Question

For the following z scores, determine whether the tail is on the right or left side of the line and find the proportion in the tail.

a. z = 2.00

b. z = 0.60

c. z = –1.30

d. z = –0.30

Answer 1

a. z=2.00

As z is positive , the tail is on the right.

To get the proportion of the tail using Excel function

=NORMSDIST (z)

Excel gives left tail area.

So to get the right tail proportion ,

P(z>2.00) =1-P(z<2.00)

=NORMSDIST (2.00)

=0.9772

1-0.9772=0.0228

Therefore the proportion of the right tail is 0.0228 or 2.28%

b. z=0.60

As z is positive,tail is on the right.

Similarly using Excel function

=NORMSDIST (0.60)

=0.7257

1-0.7257 = 0.2743

Therefore the proportion of the right tail is 0.2743 or 27.43%

c. z=-1.30

As z is negative,tail is on the left.

=NORMSDIST (-1.30)

=0.0968

Therefore the proportion of the left tail is 0.0968 or 9.68%

d. z=-0.30

As z is negative,tail is on the left.

=NORMSDIST (-0.30)

=0.3821

Therefore the proportion of the left tail is 0.3821 or 38.21%