Comparing Test Results with Z Scores Practice

An algebra test has a mean of 70 and a standard deviation of 10. Find the z score for a student who scored 85.

z = (85 - 70) / 10 = 15 / 10 = +1.50

An English test has a mean of 75 and a standard deviation of 5. Find the z score for a student who scored 65.

z = (65 - 75) / 5 = -10 / 5 = -2.00

Liam scores 88 on a chemistry test (mean = 80, standard deviation = 4). What is his z score, and what does it mean in words?

z = (88 - 80) / 4 = +2.00. Liam scored exactly 2 standard deviations above the class mean.

Jordan scored 84 in French (mean = 78, standard deviation = 4) and 88 in Spanish (mean = 82, standard deviation = 5). On which test did Jordan perform relatively better?

French z = (84 - 78) / 4 = 1.50. Spanish z = (88 - 82) / 5 = 1.20. Jordan performed relatively better in French because 1.50 is greater than 1.20.

Noah scored 58 on an economics test where the mean was 64 and standard deviation was 3. Sophia scored 70 on an accounting test where the mean was 76 and standard deviation was 4. Who performed relatively better compared to their class?

Noah: z = (58 - 64) / 3 = -2.00. Sophia: z = (70 - 76) / 4 = -1.50. Sophia performed relatively better because -1.50 is higher (closer to the mean) than -2.00.

A standardized math test has a mean of 500 and a standard deviation of 100. Using a standard normal table, what percentage of students score below a student with a score of 600?

z = (600 - 500) / 100 = +1.00. From the standard normal table, the area below z = 1.00 is 0.8413, or approximately 84.13%.