IB Maths AA HL 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 2, calculatorHard6 marks

A running club records the weekly training time, $x$ hours, and 5 km race time, $y$ minutes, for eight recreational runners. The scatter diagram of the results is shown in Figure 1.

(a)

Use a GDC to determine the Pearson product-moment correlation coefficient, $r$ and the equation of the regression line of $y$ on $x$ Give $r$ and the coefficients of the regression equation to three significant figures.

[2]

(b)

Use your regression equation from part (a) to estimate the 5 km time for a runner who trains for 20 hours per week.

[1]

(c)

A coach proposes that the club should:

recommend 20 hours of training per week because the regression predicts a faster 5 km time, claiming that adding training will cause every runner’s time to improve;
estimate the weekly training time needed by a runner targeting a 5 km time of 27.0 minutes by rearranging the regression equation from part (a).

Comment on the statistical validity of these two proposals.

[3]

Question 2

Paper 1, no calculatorHard6 marks

A health service records whether each of 300 participants has a risk factor $F$ and whether each is diagnosed with a disease $D$ Figure 1 shows the results.

A report notes that more participants diagnosed with $D$ had $F$ than did not have $F$ and concludes that diagnosis is more likely among participants with $F$

(a)

State the definition of $P(A\mid B)$ in terms of $P(A\cap B)$ and $P(B)$

[1]

(b)

Use Figure 1 to calculate $P(F\mid D)$

[1]

(c)

In light of your answer to (b), test whether $F$ and $D$ are independent and assess the report’s conclusion.

[4]

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