If Dave scores 96 in a test that has a mean score of 128 and a standard deviation of 16, what is his z-score?
Frank finishes a fun run in 156 minutes. If the mean time taken to finish the race is 120 minutes and the standard deviation is 12 minutes, what is his z-score?
For each of the following examples, find x, the test score each student received:
Iain's z-score in a test is 1, the mean mark is 62\% and standard deviation is 3\%.
Rochelle's z-score in a test is - 3, the mean mark is 80\% and standard deviation is 4\%.
A general ability test has a mean score of 100 and a standard deviation of 15.
Paul received a score of 102 in the test, find his z-score correct to two decimal places.
Georgia had a z-score of 3.13, find her score in the test, correct to the nearest integer.
Dylan scored 90\% with a z-score of 2 in English, and 78\% with a z-score of 4 in Mathematics.
In which subject was his performance better, relative to the rest of his class?
Jenny scored 81\% with a z score of - 2 in English, and 72\% with a z-score of - 4 in Mathematics. In which subject was her performance better, relative to the rest of the class?
Ray scored 12.49 in his test, in which the mean was 7.9 and the standard deviation was 1.7.
Gwen scored 30.56 in her test, in which the mean was 20.2 and the standard deviation was 2.8.
Find Ray's z-score.
Find Gwen's z-score.
Which of the two had a better performance relative to the other students in their classes?
Marge scored 43 in her Mathematics exam, in which the mean score was 49 and the standard deviation was 5. She also scored 92.2 in her Philosophy exam, in which the mean score was 98 and the standard deviation was 2.
Find Marge’s z-score in Mathematics.
Find Marge’s z-score in Philosophy.
Which exam did Marge do better in relative to the rest of her class?
Languages and Mathematics are very different disciplines, and so to compare results in the two subjects, the standard deviation is used. The mean and standard deviation of exam results in each subject are given in the table:
| Mean | Std. Deviation | |
|---|---|---|
| Languages | 60 | 7 |
| Mathematics | 67 | 8 |
A student receives a mark of 81 in Languages. How many standard deviations away from the mean is this mark?
What mark in Mathematics would be equivalent to a mark of 81 in Languages?
A student receives a mark of 86.2 in Mathematics. How many standard deviations away from the mean is this mark? Round your answer to one decimal place.
What mark in Languages would be equivalent to a mark of 86.2 in Mathematics? Round your answer to one decimal place.
If Maximilian scores 57.6, with a z score of 2, in a test that has a standard deviation of 5.8, what was the mean score?
If Han scores 43.2, with a z score of -3, in a test that has a standard deviation of 5.6, what was the mean score?
If Luke scores 68, for a z score of - 3, in a test that has a mean score of 93.5, what was the standard deviation of the test scores?
If Saoirse scores 32.5, for a z score of - 4, in a test that has a mean score of 58.5, what was the standard deviation of the test scores?