IB Maths AI 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 Paper 2

Difficulty

Easy Medium Hard

Question 1

Paper 2Easy6 marks

A city council wants to describe the repair times for 240 potholes repaired during April. It selects 12 repair records at random. For these 12 records, the lower quartile is 4 hours and the upper quartile is 8 hours. One recorded repair time is 18 hours.

(a)

State the population and the sample.

[2]

(b)

Calculate the interquartile range and determine whether the 18-hour repair time is an outlier.

[2]

(c)

The maintenance log confirms that this repair took 18 hours because a lane closure delayed the crew. State whether the value should be removed before describing the sample, giving a reason.

[2]

Question 2

Paper 2Easy5 marks

A school records the commute times of students travelling by two bus routes. Figure 1 shows box-and-whisker diagrams of the times, in minutes.

(a)

Write down the median commute time for Route A.

[1]

(b)

Calculate the interquartile range of the commute times for Route B. Give your answer in minutes.

[2]

(c)

State which route’s commute times may be normally distributed. Give one feature of its box-and-whisker diagram to support your answer.

[2]

Question 3

Paper 2Easy5 marks

A delivery service compares the delivery times for two routes. The values below summarize the box-and-whisker plots for each route. All values are in minutes.

Route	Lower whisker end	Lower quartile	Median	Upper quartile	Upper whisker end
A	12	18	24	30	36
B	10	15	20	28	40

(a)

Calculate the interquartile range for each route.

[2]

(b)

State which route has the higher median delivery time.

[1]

(c)

State which route’s delivery times may be normally distributed. Give a reason based on the symmetry of its box and whiskers.

[2]

Question 4

Paper 2Easy6 marks

A technician records the volume of water in a container as it is filled. Let $t$ be the time, in minutes, after filling begins, and let $V$ be the volume of water, in litres.

$t$	0	2	4	6	8	10	12	14
$V$	10	17	27	30	44	46	60	64

(a)

Use a GDC to calculate Pearson’s product-moment correlation coefficient, $r$ to three significant figures. Describe the direction and strength of the linear correlation.

[2]

(b)

Use a GDC to find the equation of the regression line of $V$ on $t$ giving its coefficients to four significant figures.

[1]

(c)

Use your regression line to estimate the volume of water after 9 minutes. Give your answer in litres to three significant figures.

[1]

(d)

Interpret the gradient and the vertical intercept of the regression line in this context.

[2]

Question 5

Paper 2Easy6 marks

A filling machine produces packets of dried fruit. The mass $X$ in grams, of a randomly selected packet is modelled by a normal distribution with mean $500$ g and standard deviation $4$ g.

(a)

Sketch the normal curve for $X$ Label the horizontal axis with $\mu-\sigma$ $\mu$ $\mu+\sigma$ and their corresponding masses.

[2]

(b)

Use your GDC to calculate the probability that a packet has a mass between $496$ g and $504$ g. Give your answer to four significant figures.

[2]

(c)

Use your GDC to find the mass $x$ such that $90\%$ of packets have a mass less than $x$ Give your answer to the nearest $0.1$ g.

[2]

Question 6

Paper 2Easy5 marks

A game pays the player different amounts on each play. Let $X$ be the player’s net gain, in USD, on one play. The probability distribution of $X$ is shown in Figure 1.

(a)

Write down $P(X=1)$

[1]

(b)

Show that $E(X)=0$

[3]

(c)

Hence state whether the game is fair.

[1]

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