question about calculating z score for the average of cases with disease

#1
Hello,

I want to calculate Z score for the average of cases with disease. I have normal population average and standard deviation (this is based on 50 normal cases), and I have 6 cases with disease for whom I have average and standard deviation. To calculate the z score for the average of cases with disease is the following formula correct?
Z= ( average of the 6 cases with disease- average of the 50 normal cases ) / ( standard deviation of the normal 50 cases / sqrt(6) )