Question

Find the standard deviation given...5. value is 48, mean is 59, and z-score is -2.56. value is 156, mean is 145, and z-score is 1.8

Answer 1

5. Take into account that the z-score is given by the followin formula:

Z = (x - μ)/σ

where:

x: data point = 48

μ: mean = 59

σ: standard deviation = ?

Z: z-score = -2.5

Solve the formula for σ and replace the values of the rest of the parameters, as follow:

Z = (x - μ)/σ

σ = (x - μ)/Z

σ = (48 - 59)/(-2.5)

σ = -11/(-2.5)

σ = 4.4

6. In this case, you have:

x: data point = 156

μ: mean = 145

σ: standard deviation = ?

Z: z-score = 1.8

σ = (x - μ)/Z

σ = (156 - 145)/(1.8)

σ = 6.11