|
|
Exam-Style Question on CorrelationA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 684. This question is similar to one that appeared on an IB AA Higher paper in 2021. The use of a calculator is allowed.
At a large airport, the waiting time between a plane landing and a passenger being able to get off the aircraft is dependent upon the row number of the seat that the passenger has been assigned to.
Betty, a frequent flier, took a flight to the airport on seven consecutive weekends. The following table shows the row number, \( x \), and Betty's waiting time, \( y \) minutes.
| Row number (\( x \)) | Betty’s waiting time (\( y \)) |
|---|---|
| 43 | 18 |
| 50 | 27 |
| 36 | 16 |
| 39 | 20 |
| 58 | 30 |
| 54 | 25 |
| 36 | 19 |
The relationship between \( x \) and \( y \) can be modelled by the regression line of \( y \) on \( x \) with equation \( y = mx + b \).
(a) Find the value of \( m \) and the value of \( b \).
(b) Write down the value of Pearson’s product-moment correlation coefficient, \( r \).
(c) Interpret, in context, the value of \( m \) found in part (a).
On another week, Betty takes the same flight. She has been assigned 42C, a seat in the forty second row.
(d) Use the result from part (a) to estimate Betty’s waiting time to leave the aircraft after it has landed.
|
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription. Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves. This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures. A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience. |
|
Drag this panel down to reveal the solution
A380 seating plan by S. Solberg J., CC BY 1.0, via Wikimedia Commons
The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.
The solutions to the questions on this website are only available to those who have a Transum Subscription.
Exam-Style Questions Main Page
To search the entire Transum website use the search box in the grey area below.
©1997 - 2024 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/
