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: 2.49 unusual

Explanation:

Answer 2

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

Explanation:

To calculate the Z score use the following formula

`Z=(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=(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.”