A certain raw score equals 85 and is at the 15th percentile

A certain raw score equals 85 and is at the 15^th percentile. The standard deviation is 15.27. What is the mean of the distribution? The mean equals 60. One individual scores at the 13th percentile and has a raw scored of 50. What is the standard deviation? Find the T score if the z score is -.10.

Solution

1)z-score at 15% =  -1.036433.....

so, mean + (  -1.036433 * 15.57 ) = 85.....

so, mean = 101.1373..

2) z-score at 13% is -1.126391...

so, 60 + ( -1.126391 * s.d) = 50

so, s.d = 8.877912.....

3) z -score = - 0.10 = (raw score - mean) / s.d = t-score
t-score = - 0.10.......