Z-scores

In a population distribution, a score of X = 54 corresponds to Z = 2 and a score of X = 42 corresponds to Z = -1. What are the values for the mean and standard deviation for the population?

54 - 42 = 12 2 + 1 = 3 12 = 3 SD 1 SD = 12/3 = 4 42 + 4 = 46 = M

In a population distribution, a score of X = 64 has a z score of z = .5 and a score of X = 72 has a z score of z = 1.5. What are the values for the mean and standard deviation for the population?

72 - 64 = 8 1.5 - .5 = 1 8 = 1 SD 64 - (.5 X 8) 64 - 4 60 = M

In a population with a standard deviation of σ = 6, a score of X = 33 corresponds to Z = 1.5. What is the mean?

X = μ + zσ 33 = μ + 1.5(6) 33 = μ + 9 μ = 33 - 9 μ = 24

In a population with a mean of μ = 65, a score of X = 59 corresponds to Z = -2. What is the standard deviation?

Z = X-μ /σ σ = X - μ /Z = 59-65/ -2 = -6/ -2 = 3