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IB Maths: The Normal Distribution and z-Scores (Paper 4: misconception drill)
IB Maths: The Normal Distribution and z-Scores (Paper 4: misconception drill)
IB maths normal distribution paper 4, misconception drill: ten questions fixing errors on standardising, direction, variance and standard error.
Direct answers Answers in order: 5, two standard deviations below the mean, 0.1587, 68, 90 to 110, 5, 0.1336, 4, about 9, and keep the negative sign.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: IB Maths: The Normal Distribution and z-Scores |
| Level | IB |
02 Questions (10 items)
- FoundationA score is 10 above the mean and the standard deviation is 2. A student answers z = 20. What is correct?
- FoundationWhat does a z-score of -2 mean?
- FoundationGiven the table value 0.8413 at z = 1, find the probability that Z exceeds 1.
- IntermediateWith mean 60 and standard deviation 8, which score has z = 1?
- IntermediateWith mean 100 and standard deviation 10, what range holds the middle 68 percent?
- IntermediateA distribution has variance 25. What is the standard deviation?
- ChallengeGiven the table value 0.9332 at z = 1.5, find the probability that the absolute value of Z exceeds 1.5.
- ChallengeThe standard deviation is 20 and the sample size 25. What is the standard error of the sample mean?
- ChallengeIf 2.28 percent of items are faulty, about how many of 400 sampled items are faulty?
- Error redoA student takes the absolute value of a below-average z and writes 2. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 5 | The gap is divided by the standard deviation, so 10 over 2 gives 5. |
| 2 | The score is two standard deviations below the mean | The sign says below the mean and the number counts standard deviations, not marks. |
| 3 | 0.1587 | A greater-than probability is one minus the table value. |
| 4 | 68 | One standard deviation is 8 marks, so 60 plus 8 gives 68, not 60.8. |
| 5 | 90 to 110 | The 68 percent band is one standard deviation wide, while 95 percent needs two. |
| 6 | 5 | The standard deviation is the square root of the variance, not the variance itself. |
| 7 | 0.1336 | Two tails means doubling: 1 minus 0.9332 gives 0.0668, then times two. |
| 8 | 4 | 20 divided by the square root of 25, which is 5, gives 4 rather than 20. |
| 9 | About 9 | 400 times 0.0228 is 9.12, which is about 9 items. |
| 10 | A below-average z keeps its negative sign, which records the direction | Dropping the sign loses the direction, so later table readings or inverse values go wrong. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Always subtract the mean and divide by the standard deviation first, then read the standard normal table; to go backwards, find z first and multiply by the standard deviation before adding the mean.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.