Question

The time it takes to complete a test is

normally distributed with a mean of 45
minutes and a standard deviation of 12
minutes. If Nick took an hour and 8 minutes
to complete the test, find his z-score to the
nearest hundredth of a second.
I

Answer 1

The z-score is -3.08, approximately.

Explanation:

The z-score is defined

`Z=(x - \mu)/(\sigma)`

Where
`\mu` is the mean,
`\sigma` is the standard deviation and
`x` the data value.

In this case, we have

`x=8\\\mu = 45\\\sigma=12`

Replacing values, we have

`Z=(8-45)/(12)=(-37)/(12) \approx -3.08`

Therefore, the z-score is -3.08, approximately.