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Exam-Style Question on Correlation

A mathematics exam-style question with a worked solution that can be revealed gradually

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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.

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A380 seating plan by S. Solberg J., CC BY 1.0, via Wikimedia Commons

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