Practice IB Mathematics Applications & Interpretation (AI) Topic SL 4.1—introduction to Statistics with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.1—introduction to Statistics and mirrors Paper 1, 2, 3 style where relevant.
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The table below shows the distribution of parcels delivered per day by a group of bicycle couriers surveyed during a festival week in Amsterdam.
(a) Find the mean number of parcels delivered by the couriers.
(b) Find the standard deviation of the number of parcels delivered.
(e) Find the probability that a courier chosen at random delivered or more parcels.
(f) Given that the first courier chosen at random delivered or more parcels, find the probability that both couriers delivered exactly parcels.
(g) The time spent on route-planning training by a courier is modelled by . the probability that a courier chosen at random spent at least hours on training.
(h) the expected number of couriers that spent at least hours on training.
(i) The survey was carried out by selecting every th name from an alphabetical staff list. the sampling technique used in this sampling method.
(e) Find the probability that this courier delivered or more parcels.
(f) Given that the first courier chosen at random delivered or more parcels, find the probability that both couriers delivered exactly parcels.
(g) the probability that a courier chosen at random had a delivery time lasting at least minutes.
(h) the expected number of couriers whose delivery time lasted at least minutes.
(i) the sampling technique used in this sampling method.
| Parcels | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
|---|
| Frequency | 3 | 6 | 10 | 14 | 23 | 21 | 13 | 7 | 3 |
A courier is chosen at random from the group of couriers.
A second courier is chosen at random from the group of couriers.
The time taken by the couriers to complete a standard route was normally distributed with a mean of minutes and a standard deviation of minutes.
The couriers were selected for the survey by randomly choosing names from the full company list using a computer generator.
(a) Find the mean number of parcels delivered by the couriers.
(b) Find the standard deviation of the number of parcels delivered.
(c) Find the median number of parcels delivered by the couriers.
(d) Find the interquartile range.
(e) Find the probability that this courier delivered or more parcels.
(f) Given that the first courier chosen at random delivered or more parcels, find the probability that both couriers delivered exactly parcels.
(i) the sampling technique used in this sampling method.
The table below shows the distribution of parcels delivered per shift by a group of couriers surveyed on a working day in Dublin.
| Parcels | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 4 | 6 | 12 | 18 | 25 | 17 | 10 | 5 | 3 |
(a) Find the mean number of parcels delivered by the couriers.
(b) Find the standard deviation of the number of parcels delivered.
(c) Find the median number of parcels delivered by the couriers.
The table below shows the distribution of parcels delivered per day by a group of bicycle couriers surveyed during a busy week in Copenhagen.
| Parcels | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 3 | 6 | 10 | 14 | 23 | 20 | 13 | 8 | 3 |
A courier is chosen at random from the group of couriers.
A second courier is chosen at random from the group of couriers.
The delivery times of the couriers were normally distributed with a mean of minutes and a standard deviation of minutes.
The couriers were selected for the survey by randomly choosing names from the full staff list using a computer generator.
A manager at a cycle-hire station conducted a study to determine the rental duration, in minutes, of bicycles during one afternoon. The results are displayed in the table below.
| Duration (min) | |||||
|---|---|---|---|---|---|
| Frequency | 4 | 7 | 6 | 3 |
The estimated average rental duration, calculated using class midpoints, is 24 minutes.
(a) Classify the data as either discrete or continuous.
(c) Because it was unfeasible to record every bicycle rental, the manager listed the rental forms in time order and selected every 18th form for the study. Name the sampling method employed for this study.
(d) Find the interquartile range.
(d) Find the interquartile range.
(g) the probability that a courier chosen at random took at least minutes to complete the route.
(h) the expected number of couriers whose route took at least minutes.
(b) the value of .
