Z Scores and Percentiles

Mary is a social worker who leads a treatment group of young adults diagnosed with chronic anxiety. Group members are selected for treatment based on their scores on a particular screening device, Anxiety Scale A. This instrument has a mean of 60 and a standard deviation of 12. Those scoring over 72 on Anxiety Scale A are eligible to join the treatment group.

Suppose there is a vacancy in the group that must be filled. Mary refers to her files and finds that she has a client named Jessie who qualifies for the treatment because her score on Anxiety Scale A was 76. However, there is a new client, Marvin, who was referred to the treatment center from another clinic. His records indicate that at his previous treatment center Marvin scored a 68 on Anxiety Scale B, another valid and reliable measuring instrument. Anxiety Scale B has a mean of 52 and a standard deviation of 10.

Mary is forming a new treatment group of young adults with very high anxiety levels. She will only admit those in the 95th percentile of above on Anxiety Scale A.

Question is : What is the lowest raw score that a client must have on Anxiety Scale A in order to be admitted into this new group? Also assuming some clinics use Anxiety Scale B and often refer their clients to Mary, what is the cutoff point (lowest raw score) for these clients to be admitted into the new group?

I also have a chart that is too lengthy to include with this question.. It is areas under the Standard Normal Curve (the z table) it has z scores listed and the percnet that the z equals. If I need to look up certain z scores to give you the percent please email me back with those numbers.