Answer :
Final answer:
The z-score for the data value 38.6 with a mean of 41 and standard deviation of 5.3 is approximately -0.45. The z-score calculates how many standard deviations a particular value is away from the mean in a data set.
Explanation:
The z-score in statistics is a value used to quantify the measurement of how data points are dispersed in a data set. The z-score of a data point describes how many standard deviations that data point is from the mean of the data set. You can calculate the z-score using the following formula: z = (X - μ) / σ, where X is the data point, μ is the mean of the data set, and σ is the standard deviation of the data set.
Given that your mean (μ) is 41, the value of your data point (X) is 38.6, and your standard deviation (σ) is 5.3.
Z-Score = (38.6 - 41) / 5.3 = -0.45283018867924523.
Hence, the z-score for the data value of 38.6 is approximately -0.45.
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