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 2Medium6 marks

Ridgeway College wants to estimate the usual one-way travel time of all its students. A staff member asks the first 40 students they meet as they leave the cafeteria at lunch. For these responses, the lower quartile is 18 minutes and the upper quartile is 30 minutes. One recorded travel time is 55 minutes.

(a)

Calculate the interquartile range (IQR).

[1]

(b)

Determine whether the travel time of 55 minutes is an outlier. Show a comparison with the nearest quartile.

[2]

(c)

The student confirms that 55 minutes is accurate for their usual journey, which includes a ferry crossing and a transfer. Should this value be removed when summarizing the sample? Justify your answer.

[1]

(d)

Explain one limitation of the staff member’s sampling method and suggest a more suitable sampling method.

[2]

Question 2

Paper 2Medium6 marks

Two independent fair spinners are used in a game. Spinner $X$ has four equally likely results, $1,2,3,4$ and spinner $Y$ has five equally likely results, $1,2,3,4,5$ The outcome of a round is the ordered pair $(X,Y)$ The table shows the sum for each possible outcome.

$X\backslash Y$	1	2	3	4	5
1	2	3	4	5	6
2	3	4	5	6	7
3	4	5	6	7	8
4	5	6	7	8	9

Let $E$ be the event that the sum is at least 7.

(a)

Find the theoretical probability of $E$

[2]

(b)

Find the probability of the complementary event $E'$

[1]

(c)

Find the expected number of rounds in which $E$ occurs in 80 rounds.

[1]

(d)

In a trial of 80 rounds, $E$ occurs 21 times. Find the relative frequency of $E$

[1]

(e)

Does this trial prove that the spinners are not fair? Give a reason.

[1]

The best questions are still waiting

Unlock every question in this topic, then type, photograph or draw your answer and have it marked against the markscheme. Find out where you are dropping marks.

Unlock all questions Compare Student and Student Plus