Question

Find the z-score corresponding to a score of X= 40 and the X value corresponding to z = 0.25 for each of the following distributions.

a. μ = 50 and σ = 20

b. μ = 50 and σ = 4

c. μ = 30 and σ = 8

d. μ = 30 and σ = 4

Answer 1

Solution :

Given that ,

1)

X = 40

a) Using z - score fpormula,

mean = = 50

standard deviation = = 20

Z = (x - ) / = (40 - 50) / 20 = -0.5

z - score = -0.5

b)

mean = = 50

standard deviation = = 4

Z = (x - ) / = (40 - 50) / 4 = -2.5

z - score = -2.5

c)

mean = = 30

standard deviation = = 4

Z = (x - ) / = (40 - 30) / 8 = 1.25

z - score = 1.25

d)

mean = = 30

standard deviation = = 4

Z = (x - ) / = (40 - 30) / 4 = 2.5

z - score = 2.5

2) z = 0.25

a)

mean = = 50

standard deviation = = 20

x = z * + = 0.25 * 20 + 50 = 55

X value = 55

b)

mean = = 50

standard deviation = = 4

x = z * +   = 0.25 * 4 + 50 = 51

X value = 51

c)

mean = = 30

standard deviation = = 8

x = z * +   = 0.25 * 8 + 30 = 32

X value = 32

d)

mean = = 30

standard deviation = = 4

x = z * +   = 0.25 * 4 + 30 = 31

X value = 31