IB DP Maths- MAI HL Prediction Paper 2 – 2026 Edition
IB DP Math AI HL Prediction Paper 2 – April/May 2026 Exam
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Question 1
The heights of a certain species of deer are known to have standard deviation 0.35 m. A zoologist takes a random sample of 150 of these deer and finds that the mean height of the deer in the sample is 1.42 m.
(a) Calculate a 96% confidence interval for the population mean height.
(b) Bubay says that 96% of deer of this species are likely to have heights that are within this confidence interval. Explain briefly whether Bubay is correct.
▶️Answer/Explanation
Solution :-
Part (a): Calculating the 96% Confidence Interval
Given:
- Sample mean (\(\bar{x}\)) = 1.42 m
- Population standard deviation (\(\sigma\)) = 0.35 m
- Sample size (n) = 150
- Confidence level = 96%
For a 96% confidence interval, the z-score (z) is found using a standard normal distribution table or calculator. The z-score corresponding to 96% confidence is approximately 2.054 or 2.055.
The formula for the confidence interval is:
\(\bar{x} \pm z \frac{\sigma}{\sqrt{n}}\)
Plugging in the values:
\(1.42 \pm z \frac{0.35}{\sqrt{150}}\)
Lower bound: 1.36 m
Upper bound: 1.48 m
Therefore, the 96% confidence interval is approximately (1.36 m, 1.48 m) (3 sf).
Part (b): Explanation of Bubay’s statement
Bubay is incorrect.
The confidence interval (CI) is about the population mean, not individual values.