21M.2.SL.TZ2.1

pestleMathematicsAASLPaper 221M· sl-4-4-pearsons-scatter-diagrams-eqn-of-y-on-xsource ↗

At a café, the waiting time between ordering and receiving a cup of coffee is dependent upon the number of customers who have already ordered their coffee and are waiting to receive it.

Sarah, a regular customer, visited the café on five consecutive days. The following table shows the number of customers, $x$ , ahead of Sarah who have already ordered and are waiting to receive their coffee and Sarah’s waiting time, $y$ minutes.

The relationship between $x$ and $y$ can be modelled by the regression line of $y$ on $x$ with equation $y = a x + b$ .

Find the value of $a$ and the value of $b$ .

[2]

a.i.

Write down the value of Pearson’s product-moment correlation coefficient, $r$ .

[1]

a.ii.

Interpret, in context, the value of $a$ found in part (a)(i).

[1]

On another day, Sarah visits the café to order a coffee. Seven customers have already ordered their coffee and are waiting to receive it.

Use the result from part (a)(i) to estimate Sarah’s waiting time to receive her coffee.

[2]

Markscheme / solution

$a = 0.805084 \dots$ and $b = 2.88135 \dots$

$a = 0.805$ and $b = 2.88$ A1A1

[2 marks]

a.i.

$r = 0.97777 \dots$

$r = 0.978$ A1

[1 mark]

a.ii.

$a$ represents the (average) increase in waiting time ( $0.805$ mins) per additional customer (waiting to receive their coffee) R1

[1 mark]

attempt to substitute $x = 7$ into their equation (M1)

$8.51693 \dots$

$8.52$ (mins) A1

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]