Question

A normally distributed population of test scores has a mean of 80 and a standard deviation of 5.2. What is the z score if a student scores 73?

Answer 1

$\\ \sf\longmapsto z=\dfrac{Score-Mean}{Standard\: Deviation}$

$\\ \sf\longmapsto z=\dfrac{73-80}{5.2)$

$\\ \sf\longmapsto z=\dfrac{-7}{5.2}$

$\\ \sf\longmapsto z=-1.34$

Answer 2

The z score if a student scores 73 when the mean is 80 and the standard deviation is 5.2. will be z=-1.34

What is Z-score?

Z-score (also called a standard score) gives you an idea of how far from the mean a data point is. But more technically it’s a measure of how many standard deviations below or above the population mean a raw score is.

The formula to calculate z score is given as:

$Z=\dfrac{X-\mu}{\sigma}$

Here x=73 is the score $\mu$ =80 is the mean and $\sigma$=5.2 is the standard deviation.

$Z=\dfrac{73-80}{5.2}$

$Z=-1.34$

So the value of z score will be -1.34

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