IB Maths AA HL Sl 4 12 Standardizing Normal Variables Questions

Practise IB Mathematics HL 4.12 by applying standardizing normal variables methods to questions from the Question Bank.

Exam points

Standardize a normal variable with z = (x − μ)/σ and interpret z as the number of standard deviations from the mean.
Use z-values with a normal model to find an unknown mean or standard deviation from a stated observation or probability condition.

[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.

Given that $\mathrm{P}(|\bar{X}-8| \leq k)=0.95$ , find the value of k.

EITHER
$k=1.96 \frac{\sigma}{\sqrt{n}}$ or $1.96 \operatorname{std}(\bar{X})$
k=0.877 or $1.96 \sqrt{0.2}$

OR
The expression is equivalent to
$P\left(320-40 k \leq \sum X \leq 320+40 k\right)=0.95$
k=0.875

Note: Accept any answer that rounds to 0.87 or 0.88 .
Award M1A0 if modulus sign ignored and answer obtained rounds to 0.74 or 0.75
Total

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IB Maths AA HL Sl 4 12 Standardizing Normal Variables Questions question 1