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

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Question 1

Paper 1, no calculatorEasy6 marks

A student records the average daily sunlight exposure, $x$ hours, and the height after four weeks, $y$ cm, of five seedlings of the same species.

$x$	2	3	4	5	6
$y$	11	12	17	17	18

For these data, the Pearson correlation coefficient is $r=0.93$ and the regression line of $y$ on $x$ is $y=1.9x+7.4$

(a)

State the strength and direction of the correlation. State whether this result alone shows that sunlight causes greater height.

[2]

(b)

Use the regression line to estimate the height of a seedling receiving 5 hours of sunlight per day.

[2]

(c)

Interpret the gradient of the regression line in this context.

[1]

(d)

The observed sunlight exposures range from 2 to 6 hours per day. Explain why using the regression line to estimate the height at 10 hours per day may be unreliable.

[1]

Question 2

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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