finding z score and percentile rank

Question

A researcher found that the rate of violent confrontations among the population of county jails is equal to 5.7 per 100 prisoners, with a standard deviation of 2.9. Enter the following data into Excel, and calculate the z-score and percentile rank for violent confrontations for each of the jails listed below. 

Jail           Violent  Confrontations

A                             6.5           

B                             10.2       

C                              2.9           

D                              1.7           

E                              5.9           

my main thing is i don't know is the 5.7/100 and the 2.9 is supposed to be used. or are they just giving me information.

Answer 1

Hi Jayla,

You need to use the information they gave you, because they ask you to calculate a Z-score. To calculate a Z-score, (or standard score), you need the mean and standard deviation, the formulas is the following:

Standard Score=[(original score)-(mean of all scores)]/ the standard deviation of all scores.

The first thing you need to do is use the 5 data points you were given, and plug them in the equation above.

Now you have the z-scores you were asked to calculate. Alternatively, using Excel: NORMSDIST(x) = NORMDIST(x, 0, 1, TRUE); You've just converted the original data to the standard normal distribution.

This step makes it much easier to find the percentiles, Now you can use Excel functions to find the percentile rank for the 5 jails in your data set.