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

Use the normal distribution curve with its mean and standard deviation, applying the 68–95–99.7 rule to estimate probabilities and intervals.
Use technology to calculate normal and inverse-normal probabilities, converting to standardised values and interpreting the resulting cut-off or context.

[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