IB Maths AA HL 4.9 Normal distribution Question Bank

Practise IB Mathematics SL/HL 4.9 by applying normal distribution methods to exam-style questions.

Exam points

identify the mathematical structure, variable or representation
select and apply the correct theorem, formula or algorithm
check the result using units, domain, graph or logical reasoning

[Maximum number: 3]

The random variable X has probability distribution $\operatorname{Po}(8)$ .

A random sample of 40 observations is taken from the distribution for X.

Find $\mathrm{P}(7.1<\bar{X}<8.5)$ .

EITHER

Note: M1 for normality, A1 for parameters.

OR
The expression is equivalent to $P\left(283 \leq \sum X \leq 339\right)$ where $\sum X$ is $\operatorname{Po}(320)$
= 0.840
Note: Accept 284, 340 instead of 283, 339

Accept any answer that rounds correctly to 0.84 or 0.85 .

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SL 4.9—Normal distribution question 1