IB Maths AA SL 4.1 Statistics and Probability Question Bank

Practise assessing samples, interpreting summary and regression output, calculating combined-event probabilities and applying discrete, binomial and normal distributions.

Syllabus
First assessment 2021
Topic
4.1
Level
SL

Exam points

  • identify sampling methods and bias, then extract medians, quartiles or frequencies from tables and graphs
  • choose the correct regression direction and interpret estimates, correlation or model limits in context
  • combine complements, unions and conditional probabilities using trees, Venn diagrams or event notation
  • define a discrete random variable before calculating its distribution, expectation or binomial probabilities
  • standardize normal variables or use inverse-normal values to recover probabilities, means or deviations

Covered syllabus points

SL 4.1—Sampling and dataSL 4.2—Data presentationSL 4.3—Summary statisticsSL 4.4—Correlation and regressionSL 4.5—Probability basicsSL 4.6—Combined, conditional and independent eventsSL 4.7—Discrete random variablesSL 4.8—Binomial distributionSL 4.9—Normal distributionSL 4.10—Regression x on ySL 4.11—Formal conditional probabilitySL 4.12—Standardizing normal variables

4.1 Statistics and probability - SL content question 1

[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.

Table for Question 4.1 Statistics and probability - SL content question 1 — IB Maths AA SL

Question (a)

(a)

Write down the mode of X.

[ 3 ]

Question (b)

(b)

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 ]

Question (c)

(c)

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

Simple random / Systematic / Convenience / Quota / Stratified

[ 1 ]

4.1 Statistics and probability - SL content question 2

[Maximum number: 15]

The following cumulative frequency graph shows the monthly income, I dollars, of 2000 families.

Figure for Question 4.1 Statistics and probability - SL content question 2 — IB Maths AA SL

Question (a)

(a)

Find the median monthly income.

[ 2 ]

Question (b)

(b)

Write down the number of families who have a monthly income of 2000 dollars or less.

Question (c)

(c)

Find the number of families who have a monthly income of more than 4000 dollars.

The 2000 families live in two different types of housing. The following table gives information about the number of families living in each type of housing and their monthly income I.

Table for Question (c) — IB Maths AA SL
[ 4 ]

Question (d)

(d)

Find the value of p.

[ 2 ]

Question (e)

(e)

A family is chosen at random.

[ 4 ]

Question (i)

(i)

Find the probability that this family lives in an apartment.

Question (ii)

(ii)

Find the probability that this family lives in an apartment, given that its monthly income is greater than 4000 dollars.

[ 4 ]

Question (f)

(f)

Estimate the mean monthly income for families living in a villa.

[ 3 ]
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