IB Mathematics AA HL 4.2 Statistics and Probability Question Bank

Practise IB Mathematics AA HL 4.2 by solving advanced probability, distributions, inference, hypothesis and statistical-modelling problems.

Exam points

HL syllabus concepts and methods
HL extended reasoning

Covered syllabus points

AHL 4.13 (HL)—Bayes' theorem AHL 4.14 (HL)—Random variables and probability density

[Maximum number: 3]

Amanda enters data from surveys into a database. It can be assumed that the accuracy of any survey entered is independent of all other surveys entered.
From previous records, it is known that Amanda enters 8 % of the surveys inaccurately.

Find the probability that a randomly selected survey was

entered by Amanda, given that the survey was entered inaccurately.

The following year, the accuracy of Amanda's and Bryce's work remained the same, as did the percentage of surveys entered by each of the three employees. However, Carmen's accuracy had improved and the probability that she entered a survey inaccurately was now x %.

The probability that a randomly selected survey had been entered inaccurately was now the same as the probability that Carmen made an error when entering a survey.

$\mathrm{P}(A \mid I)=\frac{\mathrm{P}(A \cap I)}{\mathrm{P}(I)}$ (or use of Bayes' formula)

\mathrm{P}(A \mid I)=\frac{0.55 \times 0.08}{0.081}

=0.543 \text { (accept } 54.3 \% \text { ) }

[Maximum number: 3]

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

(a)

$\bar{X}$ denotes the sample mean of n>1 independent observations from X.

[ 3 ]

(i)

Write down $\mathrm{E}(\bar{X})$ and $\operatorname{Var}(\bar{X})$ .

[ 2 ]

$\quad \mathrm{E}(\bar{X})=8$

A1
$\operatorname{Var}(\bar{X})=\frac{8}{n}$

(ii)

Hence, give a reason why $\bar{X}$ is not a Poisson distribution.

[ 1 ]

$\quad \mathrm{E}(\bar{X}) \neq \operatorname{Var}(\bar{X})($ for n>1)

R1

Note: Only award the R1 if the two expressions in (b)(i) are different.

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Covered syllabus points

4.2 Statistics and probability - AHL content question 1

4.2 Statistics and probability - AHL content question 2

Question (a)

Question (i)

Question (ii)