To calculate the z-score for any given sample from a population, you need to follow a simple formula:
Z = (X – μ) / σ
Where:
- Z = z-score
- X = value of the sample
- μ = mean of the population
- σ = standard deviation of the population
In this case, the population mean (μ) is 40 and the population standard deviation (σ) is 8. Therefore, when you have specific sample values, you can plug them into the formula to find their respective z-scores.
Here’s how you can compute the z-score for some example sample values:
- Example Sample 1: X = 48
- Z = (48 – 40) / 8
- Z = 8 / 8
- Z = 1
- Example Sample 2: X = 36
- Z = (36 – 40) / 8
- Z = -4 / 8
- Z = -0.5
- Example Sample 3: X = 32
- Z = (32 – 40) / 8
- Z = -8 / 8
- Z = -1
- Example Sample 4: X = 56
- Z = (56 – 40) / 8
- Z = 16 / 8
- Z = 2
So, by following these steps, you can calculate the z-scores for any sample values you have based on the population mean of 40 and standard deviation of 8. Just remember that a positive z-score indicates the sample is above the mean, while a negative z-score indicates it is below the mean.