# z-scores?

• Dec 29th 2009, 12:45 PM
kankabono
z-scores?
hi there,

could anyone help me out? i really don't understand z-scores... i have a final coming up and i can't contact my teachers because they are all on holidays.
for a given question, do i use the formula: z=(x-mean)/(standard deviation)? because when i am given the values for x, the mean, and standard deviation to find z, i always end up with a negative number or something that doesn't seem right. For example,

x= 20
Mean = 45
Standard Deviation = 12

How do I find the z-score using these values? It can't be just plugging the values into the formula. How do I use the chart? As well, what if I am not given an x values? What do I do?

thanks.
• Dec 29th 2009, 12:53 PM
pickslides
It is true that you simply plug these values into the formula above.

$z = \frac{X-\mu}{\sigma} = \frac{20-45}{12} = -2.08$

Now do you need to only find the z-score? Sometimes we need to find the probability of z being greater or less than this score.
• Dec 29th 2009, 01:04 PM
kankabono
yes. how do i find the probability, whether it is greater than or less than the z-score?
• Dec 29th 2009, 01:20 PM
pickslides
You need to use a table/chart, this online calculator is handy.

Z table - Normal Distribution