Question

For a population with a mean of u = 100 and a standard deviation of o = 20

a. Find the z-score for each of the following X values.

X = 108 X = 115 X = 130

X = 90 X = 88 X = 95

b. Find the score ( X value) that corresponds to each of the following z-scores.

z = -0.40 z = -0.50 z = 1.80

z = 0.75 z = 1.50 z = -1.25

Answer 1

Solution:

Z = (x - ) /

a)

X = 108

Z = (108 - 100) / 20 = 0.4

X = 115

Z = (115 - 100) / 20 = 0.75

X = 130

Z = (130 - 100) / 20 = 1.5

X = 90

Z = (90 - 100) / 20 = -0.5

X = 88

Z = (88 - 100) / 20 = -0.6

X = 95

Z = (95 - 100) / 20 = -0.25

b)

X = z * +

z = -0.40

X = -0.40 * 20 + 100 = 92

z = -0.50

X = -0.50* 20 + 100 = 90

z = 1.80

X = 1.80* 20 + 100 = 136

z = 0.75

X = 0.75* 20 + 100 = 115

z = 1.50

X = 1.50* 20 + 100 = 130

z = -1.25

X = -1.25* 20 + 100 = 75