Problem

Assume that the scores on a certain test are normally distributed with a mean of 100 and a standard deviation of 15. What is the z-score for a score of 130?

Answer

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Answer

Step 3: Substitute the values into the formula: \(Z = \frac{130 - 100}{15}\).

Steps

Step 1 ：Step 1: Identify the value of the score (X), the mean (\(\mu\)), and the standard deviation (\(\sigma\)). In this case, X = 130, \(\mu\) = 100, and \(\sigma\) = 15.

Step 2 ：Step 2: Use the formula for calculating the z-score: \(Z = \frac{X - \mu}{\sigma}\).

Step 3 ：Step 3: Substitute the values into the formula: \(Z = \frac{130 - 100}{15}\).

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