Question

in a normal distribution, a data value located 0.6 standard deviations below the mean has standard score:
z =

in a normal distribution, a data value located 2.4 standard deviations above the mean has standard score:
z =

in a normal distribution, the mean has standard score: z =

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Explanation:

Step1: Recall the formula for z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x\) is the data value, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. The z - score represents the number of standard deviations a data value is from the mean.

Step2: Calculate the z - score for a data value 0.6 standard deviations below the mean

If a data value is \(k\) standard deviations below the mean, then \(z=-k\). Here \(k = 0.6\), so \(z=-0.6\)

Step3: Calculate the z - score for a data value 2.4 standard deviations above the mean

If a data value is \(k\) standard deviations above the mean, then \(z = k\). Here \(k=2.4\), so \(z = 2.4\)

Step4: Calculate the z - score for the mean

If \(x=\mu\), then \(z=\frac{\mu-\mu}{\sigma}=\frac{0}{\sigma}=0\)

Answer:

\(z=-0.6\)
\(z = 2.4\)
\(z = 0\)