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?
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}, what is her z-score?
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 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?
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\%, what is this fund’s z-score?
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, what was his z-score correct to two decimal places?
If Georgia had a z-score of 3.13, what was 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?
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:
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?
| Mean | Std. Deviation | |
|---|---|---|
| Languages | 60 | 7 |
| Mathematics | 67 | 8 |
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.
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, compared to the rest of her class?
Kathleen scored 83.4 in her Biology exam, in which the mean score and standard deviation were 81 and 2 respectively. She also scored 60 in her Geography exam, in which the mean score was 46 and the standard deviation was 4.
Find Kathleen’s z-score in Biology. Round your answer to one decimal place.
Find Kathleen’s z-score in Geography. Round your answer to one decimal place.
Which exam did Kathleen do better in?
Ivan scored 55.25 in his test, in which the mean was 64.5 and the standard deviation was 2.5.
Maria scored 50.22 in her test, in which the mean was 57.9 and the standard deviation was 2.4.
Find Ivan's z-score.
Find Maria's z-score.
Whose performance was better relative to the other students in their classes?
The number of runs scored by Kenneth in each of his innings is listed below:
33,\, 32,\, 32,\, 32,\, 31,\, 32,\, 32,\, 32,\, 32,\, 32
What was his batting average?
What was his population standard deviation? Round your answer to two decimal places.
What was the z-score of his final innings score?
What was the z-score of his highest score? Round your answer to two decimal places.
Buzz’s best time in the half marathon is 90.2 minutes, while his best time in the full marathon is 185.6 minutes.
The mean time to complete the half marathon is 110 minutes with a standard deviation of 6 minutes among world class runners. What is the z-score of Buzz’s best time in the half marathon?
The mean time to complete the full marathon is 200 minutes with a standard deviation of 3 minutes among world class runners. What is the z-score of Buzz’s best time in the full marathon?
In which event does Buzz have a better 'best time', relative to world class runners?
Packets of flour are each labelled as having a mass of 1 \text{ kg}. The mass of these packets is normally distributed with a mean of 1.06 \text{ kg} and a standard deviation of 0.03 \text{ kg}.
Complete the following table:
| \text{Mass (kg)} | 1 | 1.03 | 1.06 | 1.09 | 1.12 |
|---|---|---|---|---|---|
| z\text{-score} |
What percentage of packets will have a mass less than 1.06 \text{ kg}?
The following table shows the batting average of all first class players at each of the cricket grounds:
Luke is a first class player, and has a batting average of 72.8 at the SCG. What is his z-score?
If Luke has a batting average of 88.2 at the MCG. What is his z-score?
If Luke has a batting average of 8.5 at the Gabba. What is his z-score?
If Luke has a batting average of 26.2 at the WACA. What is his z-score?
| Ground | Mean score | Standard deviation |
|---|---|---|
| \text{SCG} | 36 | 8 |
| \text{MCG} | 61 | 8 |
| \text{Gabba} | 33 | 7 |
| \text{WACA} | 59 | 8 |
At which ground does he play best relative to the other first class players?
The following table shows Christa’s results in the HSC, and the mean mark and standard deviation in each of her subjects:
Find Christa’s z-score in:
Chemistry
History
Physics
Maths
English
In which subject was Christa's performance strongest relative to her cohort?
| Subject | Mean | Std Dev. | Christa's mark |
|---|---|---|---|
| \text{Chemistry} | 41 | 9 | 2.3 |
| \text{History} | 47 | 7 | 77.8 |
| \text{Physics} | 56 | 8 | 82.4 |
| \text{Maths} | 48 | 3 | 38.7 |
| \text{English} | 60 | 2 | 58.4 |
A factory packages two types of cereal: Rainbow Crispies and Honey Combs.
A box of Rainbow Crispies has a mean mass of 600 \text{ g} with a standard deviation of 2.2 \text{ g}
A box of Honey Combs has a mean mass of 650 \text{ g} with a standard deviation of 1.4 \text{ g}
A box of Rainbow Crispies was selected at random for quality control. It had a mass of 613.2 \text{ g}. Calculate the z-score of this box.
A box of Honey Combs was selected at random for quality control. It had a mass of 653.08 \text{ g}. Calculate the z-score of this box.
Based on the z-scores, which box of cereal is closer to its marked mean mass.
Find the test scores of the following students' marks in their tests:
Rochelle's z-score in a test is - 3, the mean mark is 75\% and standard deviation is 3\%