Problem

A normal distribution has a mean of 98 and a standard deviation of 4 . Find the $z$-score for a data value of 90.
Round to two decimal places

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Answer

So, the z-score for a data value of 90 is \(\boxed{-2.00}\).

Steps

Step 1 :Given that the mean (\(\mu\)) is 98, the standard deviation (\(\sigma\)) is 4, and the data value (\(X\)) is 90.

Step 2 :The formula to calculate the z-score is \(Z = \frac{X - \mu}{\sigma}\).

Step 3 :Substitute the given values into the formula: \(Z = \frac{90 - 98}{4} = -2.0\).

Step 4 :So, the z-score for a data value of 90 is \(\boxed{-2.00}\).

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