Question

1. A population has a mean of μ = 70 and a standard deviation of σ = 12
2. 2. For the same population, find the score (X value) that corresponds to each of the following z-scores.

z = 0.50: X=_____                        z = 1.50: X=_____      z = -2.50: X=_____

z = -0.25: X=_____                      z = -0.50: X=_____    z = 1.25: X=_____

2. A sample has a mean of M = 30 and a standard deviation of s = 7. Find the z-score of for each of the following X values from this sample.

X = 32: z =_____                    X = 34: z =_____                    X = 36: z =_____

X = 28: z =_____                    X = 20: z =_____                    X = 18: z =_____

3. A sample has a mean of M = 35 and a standard deviation of s = 5. For this sample, find the X value corresponding to each of the following z-scores.

z = 0.40: X=_____      z = 1.20: X=_____      z = 2.00: X=_____

z = -0.80: X=_____     z = -0.60: X=_____     z = -1.40: X=_____

Answer 1

Solution :

a ) Given that

mean = = 70

standard deviation = = 12

z = 0.50

Using z-score formula,

x = z * +

x = 0.50 * 12 + 70

= 76

x = 76

z = 1.50

x = z * +

x = 1.50 * 12 + 70

= 88

x = 88

z =-2.50

x = z * +

x = - 2.50 * 12 + 70

= 40

x = 40

z = -0.25

x = z * +

x = -0.25 * 12 + 70

= 67

x = 67

z =-0.50

x = z * +

x = -0.50 * 12 + 70

= 64

x = 64

z =1.25

x = z * +

x = 1.25 * 12 + 70

= 85

x = 85

b ) Given that

sample mean = M = 30

sample standard deviation = s = 7

Using z-score formula,

X = 32

Z = X - M / S

= 32 -30 / 7

=0.28

Z = 0.28

X = 34

Z = X - M / S

= 34 -30 / 7

=0.57

Z = 0.57

X = 36

Z = X - M / S

= 36 -30 / 7

=0.86

Z = 0.86

X = 28

Z = X - M / S

= 28 -30 / 7

=- 0.28

Z = - 0.28

X = 20

Z = X - M / S

= 20 -30 / 7

=1.43

Z = 1.43

X = 18

Z = X - M / S

= 18 -30 / 7

=1.71

Z = 1.71

C) Given that

sample mean = M = 35

sample standard deviation = s = 5

Using z-score formula,

Z = 0.40

X = Z * S +M

X = 0.40 * 5 + 35

= 37

X = 37

Z = 1.20

X = Z * S +M

X = 1.20 * 5 + 35

= 41

X = 41

Z = 2.00

X = Z * S +M

X = 2.00 * 5 + 35

= 45

X = 45

Z = -0.80

X = Z * S +M

X = -0.80* 5 + 35

= 31

X = 31

Z = -0.60

X = Z * S +M

X = - 0.60 * 5 + 35

= 32

X = 32

Z = -1.40

X = Z * S +M

X = -1.40 * 5 + 35

= 28

X = 28