IB Maths AA HL Sl 4 9 Normal Distribution Questions

Practise using the normal curve, standard deviation and the 68–95–99.7 rule, with technology for normal and inverse-normal probabilities in applied data questions.

Exam points

Standardize a normally distributed variable and calculate lower-tail, upper-tail or interval probabilities.
Use inverse normal methods to find a boundary, percentile or unknown parameter from a specified probability.
Compare normal models or interpret probabilities and parameters in the given real-world context.

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Study SL 4.9—Normal distribution conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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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IB Maths AA HL Sl 4 9 Normal Distribution Questions question 1