Ant Length Z-Score Step by step Solution with Explanation

Your question:

Suppose that a sample of bullet ants has mean body length 2.1cm, and standard deviation 0.1cm. If an individual ant has length 2cm, what is its standardized value?

Ant Length Z-Score Answers and Explanation

Determining the Standardized Value (z-score) of a Bullet Ant

Mean Length (μ): 2.1 cm (This represents the average body length of all ants in the sample).

Standard Deviation (σ): 0.1 cm (This indicates the typical variation in body length around the mean).

z-score = (2.0 cm - 2.1 cm)

Divide by the Standard Deviation: We then divide the result from step 1 by the standard deviation (σ). This standardizes the unit and expresses the difference in terms of standard deviations.

The individual ant's body length (2.0 cm) is 1 standard deviation shorter than the average body length (2.1 cm) in the sample.

A negative z-score indicates the value falls below the mean.