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Mathematics Worksheet
🔔 Normal Distribution
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Compute a z-score.Apply the empirical rule (68-95-99.7).Find x from a given z-score.Recognise the bell-shaped curve.📚 Quick Recap
The normal distribution is the classic 'bell curve' — a continuous distribution that describes many natural phenomena, from heights to test scores, symmetric around its mean.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1The z-score for x = 95 if mean = 85 and SD = 5:
2The z-score for x = 70 if mean = 85 and SD = 5:
3By the Empirical Rule, the % within 3 SD of the mean is about:
4If mean = 200, SD = 25 and z = −1.5, then x =:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5A z-score = (x − mean) / .
6The z-score for x = 95, mean 85, SD 5 is .
7Find the z-score for x = 95 if mean = 85 and SD = 5.
8Find the z-score for x = 70 if mean = 85 and SD = 5.
9By the Empirical Rule, what % of values fall within 3 SD of the mean?
🚀 Section C · Challenge ● CHALLENGE 5
10If mean = 200, SD = 25 and z = −1.5, find x.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-A 2-A 3-A 4-A | 5 SD 6 2 7 = 2 8 = −3 9 = About 99.7% | 10 = 162.5