Question

A sample has a mean of M = 30 and a standard

deviation of s = 8. Find the z-score for each of the

following X values from this sample.

X = 32 X = 34 X = 36

X = 28 X = 20 X = 18

Answer 1

a)

Here, μ = 30, σ = 8 and x = 32. We need to compute P(X <= 32). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (32 - 30)/8 = 0.25

b)
Here, μ = 30, σ = 8 and x = 34. We need to compute P(X <= 34). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (34 - 30)/8 = 0.5

c)

Here, μ = 30, σ = 8 and x = 36. We need to compute P(X <= 36). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (36 - 30)/8 = 0.75

d)

Here, μ = 30, σ = 8 and x = 28. We need to compute P(X <= 28). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (28 - 30)/8 = -0.25

e)

Here, μ = 30, σ = 8 and x = 20. We need to compute P(X <= 20). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (20 - 30)/8 = -1.25

f)

Here, μ = 30, σ = 8 and x = 18. We need to compute P(X <= 18). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (18 - 30)/8 = -1.5