IB Maths AA HL 4.1 Statistics and Probability Sl Content Questions

Practise IB Mathematics AA HL 4.1 by analysing distributions, inference, regression and probability models with precise assumptions.

Exam points

HL syllabus concepts and methods
HL extended reasoning

Covered syllabus points

SL 4.1—Sampling and data SL 4.2—Data presentation SL 4.3—Summary statistics SL 4.4—Correlation and regression SL 4.5—Probability basics SL 4.6—Combined, conditional and independent events SL 4.7—Discrete random variables SL 4.8—Binomial distribution SL 4.9—Normal distribution SL 4.10—Regression x on y SL 4.11—Formal conditional probability SL 4.12—Standardizing normal variables

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Study 4.1 Statistics and probability - SL content conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[Maximum number: 6]

A supermarket analyses the shopping habits of its customers.
The number of times, X, each customer visits the supermarket in a week is given by the following probability distribution.

(a)

Find the value of a.

[ 2 ]

(b)

Write down the mode of X.

[ 1 ]

(c)

Find the mean of X.

The manager wants to know why customers come to their supermarket. They survey the first 50 customers to arrive at the supermarket on a particular day.

[ 2 ]

(d)

Identify which one of the following best describes the manager's sampling method. Circle your answer.

Simple random / Systematic / Convenience / Quota / Stratified

[ 1 ]

[Maximum number: 4]

The continuous random variable X has a probability density function given by

f(x)=\left\{\begin{array}{cc} k \sin \left(\frac{\pi x}{6}\right), & 0 \leq x \leq 6 \\ 0, & \text { otherwise } \end{array}\right.

(a)

Hence state the interquartile range of X.

[ 2 ]

from (c)(i) $Q_{1}=2$
as the graph is symmetrical about the middle value $x=3 \Rightarrow Q_{3}=4$
so interquartile range is
4-2
=2

(b)

Calculate $P(X \leq 4 \mid X \geq 3)$ .

[ 2 ]

$\quad P(X \leq 4 \mid X \geq 3)=\frac{P(3 \leq X \leq 4)}{P(X \geq 3)}$ $=\frac{\frac{1}{4}}{\frac{1}{2}}$ $=\frac{1}{2}$

[Maximum number: 4]

There are 75 players in a golf club who take part in a golf tournament. The scores obtained on the 18th hole are as shown in the following table.

(a)

One of the players is chosen at random. Find the probability that this player's score was 5 or more.

[ 2 ]

$\quad \mathrm{P}(5$ or more $)=\frac{29}{75}(=0.387)$
Marking guidance:

[2 marks]

(b)

Calculate the mean score.

[ 2 ]

mean score $=\frac{2 \times 3+3 \times 15+4 \times 28+5 \times 17+6 \times 9+7 \times 3}{75}$
(M1)
$=\frac{323}{75}(=4.31)$

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