Question

For a population with a standard deviation of σ, find the z-score for each of the following locations in the distribution.

a) Z-score for location 1
b) Z-score for location 2
c) Z-score for location 3
d) Z-score for location 4

Answer 1

To calculate the z-score of a specific location in a distribution, the formula z = (x - μ) / σ is used. The numerical z-scores cannot be determined without knowing the particular values and the mean even if the standard deviation σ is known.

Step-by-step explanation:

To calculate a z-score, you must know the specific value in the distribution you are working with (which is not provided in this context), the population mean (μ), and the population standard deviation (σ). The formula for calculating a z-score is:

z = (x - μ) / σ

where:

• x is the value in the distribution
• μ is the mean of the distribution
• σ is the standard deviation of the distribution

Given just the standard deviation σ, you cannot find the numerical z-scores without the actual values (x) and the mean (μ). For example, if the mean (μ) is 5 and the value (x) is 11 and the standard deviation (σ) is 2, the z-score for this location would be calculated as follows:

z = (11 - 5) / 2 = 3

This means that the value of 11 is 3 standard deviations above the mean on the distribution.