In a calculus class, Jack Hartig scored 4 on a quiz for which the class mean and standard deviation were 2.9 and 2.1 , respectively. Norm Alpina scored 8 on another quiz for which the class mean and standard deviation were 6.5 and 1.9 , respectively. Relatively speaking, which student did better? Make use of z-scores.

Answer: Norm Alpina did better with z-score 0.79

Step-by-step explanation:

Z score formula = (raw score - mean) / standard deviation

For Jack Hartig,

score = 4; mean = 2.9; standard deviation = 2.1

Hence, Z score = (4 - 2.9) / 2.1

= 1.1/2.1

= 0.52

For Norm Alpina,

score = 8; mean = 6.5; standard deviation = 1.9

Hence, Z score = (8 - 6.5) / 1.9

= 1.5/1.9

= 0.79

Relatively, Norm Alpina did better for having Z score 0.79