I'm in Statistics and I'm having a hard time with this problem. I keep on trying it but I keep messing up somewhere. Could someone please help?

A bank's loan officer rates applicants for credit. The ratings are normally distributed with mean of 200 and standard deviation of 50. If an applicant was randomly selected, find D6 (decile 6) the score which separates the lower 60% from the top 40%.

Thanks so much for your help!!

:D

Well, you know that 5 deciles lie below the mean, so all you need to solve for is the 1 decile (10%) above. If z=(X-mean)/Standard deviation then, z = (X - 200)/50 and the z value for the additional 10% is approximately .25 from z table (don't remember exactly how to extrapolate the exact z value from the table). So .25 = (X - 200)/50 multiply both sides by 50 to get 12.5 = X - 200, add 200 to each side to get x = 212.5. Remember this is an approximation because the actual z value is between .25 and .26.