Question 5.92

62. You can compare observations from different normal distributions if you measure in standard deviations away from the mean. Scores expressed in standard deviation units are called standard scores (or z-scores), and tables and technology commands can convert -scores into percentiles. A -score that is more than 3 or less than 23 would definitely be considered an outlier.

  1. Scores on the ACT college entrance exam in a recent year were roughly normal, with a mean of 21.2 and a standard deviation of 4.8. Jermaine scores 27 on the ACT. Express his score in standard deviation units by calculating

  1. Scores on the SAT Reasoning college entrance exam in the same year were roughly normal, with mean 1511 and standard deviation 194. Tonya scores 1718 on the SAT. What is her standard score?
  2. Assuming that the ACT and the SAT tests measure the same thing, did Jermaine or Tonya have the better performance?