Question

I’ve developed a paper and pencil aptitude test for curling called the Holistic Aptitude for Curling test. As I’ve constructed it, the (arithmetic) mean score is 86 with a standard deviation of 12. Taylor scored precisely 100 when she took the test but because of the rather arbitrary mean and standard deviation she’s having difficulty interpreting how well she did. She’s been to university in the US so she’s familiar with a couple of other types of scores. Answer each of her following questions to help her get a sense of what her score means.

(a) If the HAC was like an IQ score (mean = 100, standard deviation = 15) what would my score be?

(b) If the HAC were like the old style SAT scores (Mean = 500, standard deviation = 100) what would my score be?

(c) Based on Taylor’s HAC score, how would you describe her aptitude for curling (be precise)

Answer 1

We know that

z score =(X-mean)/standard deviation =(100-86)/12 =1.17

Part a.

Corresponding score =mean+z*standard deviation =100+1.17*15 =117.55

Part b.

Corresponding score =mean+z*standard deviation =500+1.17*100 =617

Part c.

since z score of 1.17 corresponds to 88th percentile (Using Excel formula ''=NORMSDIST(1.17)''), this tells us that her aptitude is better than 88% of her peers.

Hope this will be helpful. Thanks and God Bless You:) If any query in the solution, please post in comments.