Question

Jack and Jill are both enthusiastic players of a certain computer game. Over the past year, Jack’s mean score when playing the game is 12,400 with a standard deviation of 1500. During the same period, Jill’s mean score is 14,200, with a standard deviation of 2000. They devise a fair contest: each one will play the game once, and they will compare z-scores. Jack gets a score of 14,000, and Jill gets a score of 16,000. Who won the contest, and what were each of their z-scores

Answer 1

Jack won because he has the highest z score.

Their z scores was:

For Jack = 1.07

For Jill = 0.9

Explanation:

Solving using z score formula

z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation.

For Jack:

Jack's mean score when playing the game is 12,400 with a standard deviation of 1500. Jack gets a score of 14,000

Jack's z score = 14000 - 12400/1500

= 1.06667

Approximately = 1.07

For Jill:

During the same period, Jill's mean score is 14,200, with a standard deviation of 2000. Jill gets a score of 16,000.

Jill's z score :

16000 - 14200/2000

= 0.9

Therefore, the person with the highest z score won and that is Jack.