Final answer:
The z-score for a data value of 163 in a normal distribution with a mean of 132 and a standard deviation of 9 is approximately 3.44, which reflects that the value is 3.44 standard deviations above the mean.
Step-by-step explanation:
Calculating the Z-Score
To find the z-score for a data value in a normal distribution, we use the z-score formula:
z = (X - μ) / σ
Where:
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- X is the data value
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- μ is the mean
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- σ is the standard deviation
Given a mean (μ) of 132, a standard deviation (σ) of 9, and a data value (X) of 163:
z = (163 - 132) / 9
z = 31 / 9
z ≈ 3.44
The z-score of approximately 3.44 indicates that the data value of 163 is about 3.44 standard deviations above the mean of the distribution.