Question

given ( x = 74, mu = 64.8 ), and ( sigma = 3.6 ), indicate on the curve where the given ( x ) value would be.
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Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{X-\mu}{\sigma}\). Given \(X = 74\), \(\mu=64.8\), and \(\sigma = 3.6\).
Substitute the values into the formula: \(z=\frac{74 - 64.8}{3.6}\)

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Step2: Analyze the position

Since the mean \(\mu = 64.8\) and the standard deviation \(\sigma=3.6\), a z - score of approximately \(2.56\) means the value \(X = 74\) is about \(2.56\) standard deviations above the mean.

Answer:

The point should be moved to the right (above the mean) on the normal - distribution curve. Specifically, since \(z=\frac{74 - 64.8}{3.6}\approx2.56\), it is approximately \(2.56\) standard deviations above the mean of \(64.8\).