A test in your AP History class has a mean of 71, and a standard deviation of 4. so, the z-score of 76 is 1.2
How to get the z scores?
If we've got a normal distribution, then we can convert it to a standard normal distribution and its values will give us the z score.
If we have
[tex]X \sim N(\mu, \sigma)[/tex]
(X is following a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] ) then it can be converted to a standard normal distribution as
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
A test in your AP History class has a mean of 71, and a standard deviation of 4.
x = 76
mean = 71
standard deviation=4
therefore,
[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]
[tex]z = (76-71)/4\\\\\z=(5)/4\\\\z=(1.2)[/tex]
Learn more about z-score here:
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