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