IB Maths AA SL Topic 4: Statistics and probability questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

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Question 1

Paper 2, calculatorHard6 marks

A small business records its advertising expenditure, $x$ in hundreds of dollars, and the number of enquiries received in a week, $y$ for five weeks.

$x$	1	3	5	7	9
$y$	3	8	4	10	6

(a)

Determine the regression line of $x$ on $y$ giving its coefficients to three significant figures.

[2]

(b)

Use your regression line from part (a) to estimate the advertising expenditure when $y=7$ Give your answer in hundreds of dollars.

[1]

(c)

A manager wishes to estimate $y$ when $x=9$ She rearranges the line from part (a) and obtains $y=14.4$

Determine a regression estimate you would use instead, and explain why the manager’s value should not be treated as the regression estimate for predicting $y$ from $x$

[3]

Question 2

Paper 2, calculatorHard6 marks

A box contains 12 counters, each of which is red or blue. The number of red counters is $r$ where $r\in\mathbb{Z}$ and $1\leq r\leq 11$ Two counters are selected successively without replacement.

The probability that the two counters are the same colour is $\frac{17}{33}$

(a)

Determine the possible values of $r$

[2]

(b)

It is also known that the probability that the first counter is red, given that the second counter is red, is $\frac{3}{11}$

(i)

Determine $r$

[2]

(ii)

Hence determine the probability that exactly one of the two counters is red.

[2]

Question 3

Paper 1, no calculatorHard6 marks

In a production run, the number of packets with faulty seals is modelled by $X\sim B(n,p)$ where $n$ and $p$ are unknown. The mean of $X$ is $3$ and its variance is $2.1$

(a)

Determine $n$ and $p$

[4]

(b)

In a separate check, an inspector selects 10 packets without replacement from a lot of 20 packets, of which exactly 6 have faulty seals. A supervisor uses the values of $n$ and $p$ from part (a) to model the number of faulty packets in the check. Comment on whether this is appropriate.

[2]

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