what is the percentile rank of a score of 172

Question

a criminologist developed a test to measure recidivism, where low scores indicated a lower probability of repeating the undesirable behavior. The test is normed so that it has a mean of 140 and a standard deviation of 40.

Answer 1

The z-score would be computed by the following formula:

 

z = (x - μ) / σ 

 

where μ is the population mean and σ is the population standard deviation.

 

z = (172 - 140) / 40 = 0.8

 

From a normal distribution table, this would correspond to a probability of 0.7881.

 

The percentile rank would be 78.8%.