To find the z-score for a specific data item in a normally distributed dataset, you can use the formula:
Z = (X - μ) / σ
Where:
- X is the value of the data item,
- μ is the mean of the dataset,
- σ is the standard deviation of the dataset.
Let's calculate the z-score for the 3rd data item (13.29) using the given dataset:
Mean (μ) = (10.30 + 4.74 + 13.29 + 5.93 + 7.96 + 12.14 + 7.85 + 8.62 + 1.05 + 7.45) / 10 = 7.138
Standard Deviation (σ) = sqrt(((10.30 - 7.138)^2 + (4.74 - 7.138)^2 + ... + (7.45 - 7.138)^2) / 10) = 3.108
Now, plug these values into the z-score formula:
Z = (13.29 - 7.138) / 3.108 ≈ 1.979
So, the z-score for the 3rd data item is approximately 1.979. However, this value is not provided in the answer choices. It seems there might be a mistake in the provided options or in the calculation.
