Question

A study of persons (N = 1170) indicted for murder in Kentucky revealed that each individual had an average number of 1.69 prior felony arrests. The standard deviation was 2.6.

a. Determine the z score for a murder defendant who had two prior felony arrests. Under the normal curve, what statement could you make about this z score.

Answer 1

given :- N=1170

mean =1.69

standard deviation = 2.6

(a) z-score for a murder defendant who had two prior felony arrests is given by the formula:-

  

for two prior felony i.e. x=2

Remarks:-

• A z-score describes the position of a raw score in terms of its distance from the mean, when measured in standard deviation units. The z-score is positive if the value lies above the mean, and negative if it lies below the mean.
• The value of the z-score tells you how many standard deviations you are away from the mean. If a z-score is equal to 0, it is on the mean.
• A positive z-score indicates the raw score is higher than the mean average. For example, if a z-score is equal to +1, it is 1 standard deviation above the mean.
• A negative z-score reveals the raw score is below the mean average. For example, if a z-score is equal to -2, it is 2 standard deviations below the mean.

Conclusion:-

z-score for a murder defendant who had prior felony arrests is calculated as 0.1192. which is positive so we conclude that under the normal curve , z-score is 0.1192 standard deviation above the mean (right to the mean).