Question

A sample data set has a mean of 122.3 and a standard deviation of 18.5. Convert a score of 168.4 to a z score and determine if the score is “usual” or “unusual.”

Answer 1

Answer:

$Z=2.49$ and this Z-score is “unusual.”

Step-by-step explanation:

To calculate the Z score use the following formula

$Z=\frac{x-\mu}{\sigma}$

Where

μ is the average

$\sigma$ is the standard deviation

x is the data to which we will calculate the z-score

In this case

$\mu = 122.3\\\\\sigma= 18.5\\\\x =168.4$

So

$Z=\frac{168.4-122.3}{18.5}$

$Z=2.49$

A z-score is unusual if $Z> 2$ or $Z < -2$

Finally

$Z=2.49$ and this Z-score is “unusual.”