Question

If a vertical line is drawn through a normal distribution at each of the following z-score locations, then determine whether the tail is on the left side or the right side of the line and determine what proportion of the distribution is located in the tail.

a. z = +1.00 b. z = +0.50 c. z = -1.50 d. z = -2.00

Answer 1

(a)

Z = + 1.00

Since Z is positive, the tail is on th Right Side of the line.

Table of Area Under Standard Normal Curve gives area corresponding to Z + 1.00 as area = 0.3413

So,

the proportion of the distribution located in the tail = 0.50 - 0.3413 = 0.1587

(b)

Z = + 0.50 Since Z is positive, the tail is on the Right Side of the line.

Table of Area Under Standard Normal Curve gives area corresponding to Z = + 0.50 as area = 0.1915

So,

the proportion of the distribution located in the tail = 0.50 - 0.1915 = 0.3085

(c)

Z = - 1.50

Since Z is negative, the tailis on the Left Side of the line.

Table of Area Under Standard Normal Curve gives area corresponding to Z = - 1.50 as area = 0.4332

So,

the proportion of the distribution located in the tail = 0.50 - 0.4332 = 0.0668

(d)

Z = - 2.00

Since Z is negative, the tailis on the Left Side of the line.

Table of Area Under Standard Normal Curve gives area corresponding to Z = - 2.00 as area = 0.4772

So,

the proportion of the distribution located in the tail = 0.50 - 0.4772 = 0.0228