IB Maths AA HL 4.12 Standardizing normal variables Question Bank

Practise IB Mathematics SL/HL 4.12 by applying standardizing normal variables 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.

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 $1.96 \operatorname{std}(\bar{X})$
(M1)(A1)
k=0.877 or $1.96 \sqrt{0.2}$

OR
The expression is equivalent to
$P\left(320-40 k \leq \sum X \leq 320+40 k\right)=0.95$
(M1)
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

All question bank results loaded

SL 4.12—Standardizing normal variables question 1