If Dave scores 96 in a test that has a mean score of 128 and a standard deviation of 16, find 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, find his z-score.
Christa is 157 \text{ cm} tall. If the average height in her class is 141 \text{ cm} and the standard deviation is 8 \text{ cm}, find her z-score.
If Iain's z-score in a test is 1, the mean mark is 62\% and standard deviation is 3\%, find X, his test score.
A particular investment fund has returned 17.2\% p.a. on average over a period. If the mean return of all investment funds over the same period was 8\% p.a. and the standard deviation was 2.3\%, find this fund’s z-score.
If Rochelle's z-score in a test is - 3, the mean mark is 75\% and standard deviation is 3\%, find her test score, X.
If Aaron's z-score in a test is 3.6, the mean mark is 75\% and standard deviation is 3\%, find his test score, X.
If Sean's z-score in a test is - 1.1, the mean mark is 76\% and standard deviation is 3\%, find his test score, X.
A general ability test has a mean score of 100 and a standard deviation of 15.
If Paul received a score of 102 in the test, find his z-score, correct to two decimal places.
If Georgia had a z-score of 3.13, find her score in the test, correct to the nearest integer.
If Maximilian scores 57.6, with a z-score of 2, in a test that has a standard deviation of 5.8, find the mean score.
Maria scored 80\% with a z-score of 4 in Physics, and 73\% with a z-score of 1 in Chemistry. In which subject did she get the better result?
Deborah scored 86\% with a z-score of 3 in Music, and 73\% with a z-score of 2 in History. In which subject did she get the better result?
Xanthe scored 81\% with a z-score of -2 in English, and 76\% with a z-score of -3 in Mathematics. In which subject did she get the better result?
Valentina scored 89\% with a z-score of -1 in Mathematics, and 77\% with a z-score of -3 in English. In which subject did she get the better result?
The following table shows the finish times of a runner competing in a 10\text{ km} race in two different years:
| \text{Year} | \text{Time} \\ \text{(mins)} | \text{Mean} \\ \text{ (mins)} | \text{Standard deviation} \\ \text{(mins)} |
|---|---|---|---|
| 2017 | 75 | 78 | 1 |
| 2018 | 59 | 63 | 4 |
How many standard deviations below the mean was the runner's finish time in 2017?
How many standard deviations below the mean was the runner's finish time in 2018?
In which year did the runner perform the best relative to the other runners in the race?
The following table shows the marks obtained by a student in two subjects:
| Subject | Mark | Mean | Standard deviation |
|---|---|---|---|
| \text{Science} | 90 | 50 | 10 |
| \text{Mathematics} | 97 | 84 | 13 |
How many standard deviations above the mean was the student's score in Science?
How many standard deviations above the mean was the student's score in Mathematics?
In which subject did the student perform better?
Nadia scored 34.5 in her Mathematics exam, where the mean score was 42 and the standard deviation was 5. She scored 71.2 in her History exam, where the mean score was 88 and the standard deviation was 6.
Find the z-score of Nadia’s Mathematics results.
Find the z-score of Nadia’s History results.
In which subject did Nadia perform better?
Eileen scored 88.5 in her Physics exam, where the mean score was 78 and standard deviation was 7. She scored 62 in her History exam, where the mean score was 46 and the standard deviation was 5.
Find the z-score of Eileen's Physics results.
Find the z-score of Eileen's History results.
In which subject did Eileen perform better?
John’s best time in the half marathon is 93 minutes and his best time in the full marathon is 216.2 minutes. Among other runners, the mean time to complete the half marathon is 119 minutes with a standard deviation of 5 minutes, and the mean time to complete the full marathon is 225 minutes with a standard deviation of 4 minutes.
What is the z-score of John’s best time in the half marathon?
What is the z-score of John’s best time in the full marathon?
In which event does John have the better time relative to the other runners?
Frank got 53.58 in his test, in which the mean was 58.9 and the standard deviation was 1.4.
Emma got 64.6 in her test, in which the mean was 71.4 and the standard deviation was 1.7.
Find the z-score of Frank's test results.
Find the z-score of Emma's test results.
Who performed better relative to the others who did the tests?
Tracy scored 12.46 in her test, in which the mean was 7.9 and the standard deviation was \\1.9.
William scored 24.3 in his test, in which the mean was 19.9 and the standard deviation was 1.1.
Find the z-score of Tracy's test results.
Find the z-score of William's test results.
Who performed better relative to the others who did the tests?
The mean and standard deviation of exam results in each subject are given below.
| Mean | Standard deviation | |
|---|---|---|
| English | 75 | 9 |
| Mathematics | 72 | 8 |
A student receives a mark of 93 in English. How many standard deviations away from the mean is this mark?
What mark in Mathematics would be equivalent to a mark of 93 in English?
A student receives a mark of 53.6 in Mathematics. How many standard deviations away from the mean is this mark?
What mark in English would be equivalent to a mark of 53.6 in Mathematics?
Heart rates are often used to measure an individual's athletic capacity. The mean and standard deviation of resting heart rates for two groups are given below:
A person from Group 1 had a heart rate of 106\text{ bpm}. How many standard deviations away from the mean is this person's heart rate?
What heart rate in Group 2 would show a relatively equivalent athletic capacity to a heart rate of 106 in Group 1?
A person from Group 2 had a heart rate of 73.2\text{ bpm}. How many standard deviations away from the mean is this person's heart rate?
What heart rate in Group 1 would show a relatively equivalent athletic capacity to a heart rate of 73.2 in Group 2?
| \text{Mean} \\ \text{(bpm)} | \text{Standard deviation} \\ \text{(bpm)} | |
|---|---|---|
| Group 1 | 76 | 10 |
| Group 2 | 78 | 8 |
The attached table shows the batting average of all first class cricket players at each of the grounds:
If Isabelle has a batting average of 240.20 at the WACA, what is her z-score?
If Isabelle has a batting average of 222.6 at the Gabba, what is her z-score?
If Isabelle has a batting average of 99 at the MCG, what is her z-score?
If Isabelle has a batting average of 156.6 at the SCG, what is her z-score?
At which ground does she play best relative to the other first class players?
| Ground | Mean score | Standard deviation |
|---|---|---|
| \text{WACA} | 194 | 11 |
| \text{Gabba} | 194 | 11 |
| \text{MCG} | 189 | 18 |
| \text{SCG} | 189 | 12 |
Eileen received a mark of 55 for her History assignment and 65 for her Philosophy assignment. The following list shows the marks of all her classmates for each of the assignments:
-
History: 51, 55, 22, 10, 34, 54, 60, 52, 31, 47, 48, 57, 35, 21, 30
Philosophy: 54, 70, 45, 43, 70, 82, 57, 41, 43, 59, 53, 54,40,65,46
What was the mean mark for the History assignment, correct to two decimal places?
What was the standard deviation for the History assignment, correct to two decimal places?
What was the mean mark for the Philosophy assignment, correct to two decimal places?
What was the standard deviation for the Philosophy assignment, correct to two decimal places?
What was Eileen’s z-score for the History assignment, correct to two decimal places?
What was Eileen’s z-score for the Philosophy assignment, correct to two decimal places?
In which assignment did she perform the best?
The following table records the lengths of fish caught by a group of fishermen on a particular day:
| \text{Type} | \text{Length (cm)} |
|---|---|
| \text{Yellowfin Bream} | 29,24,29,28,25 |
| \text{Flathead} | 35,33,32,38,38,34 |
Calculate the mean length of Yellowfin Bream caught by the fishermen.
Calculate the standard deviation of the length of a Yellowfin Bream, correct to two decimal places.
If Evan catches a 33\text{ cm} Yellowfin Bream, calculate the z-score of this fish, correct to one decimal place.
Calculate the mean length of Flathead caught by the fishermen.
Calculate the standard deviation of the length of Flathead, correct to two decimal places.
If Evan catches a 37\text{ cm} Flathead, calculate the z-score of this fish, correct to one decimal place.
Which of the fish Evan caught is longer relative to the species caught by the others?