the mean and the standard deviation of the wages of 1000 factory workers are $20,600 and $2,400 respectively. if a worker's annual wage is $20,000, find and interpret the worker's sample z-score.
To find the worker's sample z-score, we need to use the formula:
z-score = (x - μ) / σ
Where:
x = worker's annual wage = $20,000
μ = mean of the wages = $20,600
σ = standard deviation of the wages = $2,400
Plugging in the given values:
z-score = (20,000 - 20,600) / 2,400
Now let's calculate the z-score:
z-score = -0.25
Interpreting the worker's sample z-score:
A z-score is a measure of how many standard deviations an individual value is away from the mean. In this case, the worker's z-score is -0.25. Since the z-score is negative, it means that the worker's annual wage of $20,000 is slightly below the mean wage of $20,600. The magnitude of the z-score indicates the relative distance from the mean in terms of standard deviations. In this case, the worker's wage is approximately 0.25 standard deviations below the mean.