Questions - AQA - A-Level Maths

Calculate the probability that, on any particular day when Gary travels to work, he:
1. does not use his car;
2. uses his car only;
3. uses a bus.
On any day, the probability that Larry travels to work with Gary is 0.9 when Gary uses his car only, is 0.7 when Gary uses both his car and a bus, and is 0.3 when Gary uses a bus only.
1. Calculate the probability that, on any particular day when Gary travels to work, Larry travels with him.
2. Assuming that option choices are independent from day to day, calculate, to three decimal places, the probability that, during any particular week (5 days) when Gary travels to work every day, Larry never travels with him.

AQA S1 2009 January Q5

8 marks Moderate -0.3

5 The times taken by new recruits to complete an assault course may be modelled by a normal distribution with a standard deviation of 8 minutes. A group of 30 new recruits takes a total time of 1620 minutes to complete the course.

Calculate the mean time taken by these 30 new recruits.
Assuming that the 30 recruits may be considered to be a random sample, construct a $98 \%$ confidence interval for the mean time taken by new recruits to complete the course.
Construct an interval within which approximately $98 \%$ of the times taken by individual new recruits to complete the course will lie.
State where, if at all, in this question you made use of the Central Limit Theorem.

AQA S1 2009 January Q6

15 marks Moderate -0.3

6 [Figure 1, printed on the insert, is provided for use in this question.]
For a random sample of 10 patients who underwent hip-replacement operations, records were kept of their ages, $x$ years, and of the number of days, $y$, following their operations before they were able to walk unaided safely.

Patient	$\mathbf { A }$	$\mathbf { B }$	$\mathbf { C }$	$\mathbf { D }$	$\mathbf { E }$	$\mathbf { F }$	$\mathbf { G }$	$\mathbf { H }$	$\mathbf { I }$	$\mathbf { J }$
$\boldsymbol { x }$	55	51	62	66	72	59	78	55	62	70
$\boldsymbol { y }$	34	33	39	49	48	43	51	41	46	51

On Figure 1, complete the scatter diagram for these data.
Calculate the equation of the least squares regression line of $y$ on $x$.
Draw your regression line on Figure 1.
In fact, patients H, I and J were males and the other 7 patients were females.
1. Calculate the mean of the residuals for the 3 male patients.
2. Hence estimate, for a male patient aged 65 years, the number of days following his hip-replacement operation before he is able to walk unaided safely.

AQA S1 2009 January Q7

12 marks Moderate -0.8

7 The proportion of passengers who use senior citizen bus passes to travel into a particular town on 'Park \& Ride' buses between 9.30 am and 11.30 am on weekdays is 0.45 . It is proposed that, when there are $n$ passengers on a bus, a suitable model for the number of passengers using senior citizen bus passes is the distribution $\mathrm { B } ( n , 0.45 )$.

Assuming that this model applies to the 10.30 am weekday 'Park \& Ride' bus into the town:
1. calculate the probability that, when there are $\mathbf { 1 6 }$ passengers, exactly 3 of them are using senior citizen bus passes;
2. determine the probability that, when there are $\mathbf { 2 5 }$ passengers, fewer than 10 of them are using senior citizen bus passes;
3. determine the probability that, when there are $\mathbf { 4 0 }$ passengers, at least 15 but at most 20 of them are using senior citizen bus passes;
4. calculate the mean and the variance for the number of passengers using senior citizen bus passes when there are $\mathbf { 5 0 }$ passengers.
1. Give a reason why the proposed model may not be suitable.
2. Give a different reason why the proposed model would not be suitable for the number of passengers using senior citizen bus passes to travel into the town on the 7.15 am weekday 'Park \& Ride' bus.

AQA S1 2011 January Q1

7 marks Easy -1.3

Estimate, without undertaking any calculations, the value of the product moment correlation coefficient between the variables $x$ and $y$ for each of the two scatter diagrams. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{(i)} \includegraphics[alt={},max width=\textwidth]{156f9453-ebc6-4406-b5bc-08d1918ebc62-02_487_652_733_356}
\end{figure} \includegraphics[max width=\textwidth, alt={}, center]{156f9453-ebc6-4406-b5bc-08d1918ebc62-02_576_714_733_1153}
The table gives the circumference, $x$ centimetres, and the weight, $y$ grams, of each of 12 new cricket balls.
$\boldsymbol { x }$ 22.5 22.7 22.6 22.4 22.5 22.8 22.6 22.7 22.8 22.4 22.9 22.6
$\boldsymbol { y }$ 160.3 159.4 157.8 158.0 157.3 159.8 158.3 159.6 161.3 156.4 162.5 161.2
1. Calculate the value of the product moment correlation coefficient between $x$ and $y$.
2. Assuming that the 12 balls may be considered to be a random sample, interpret your value in context.

AQA S1 2011 January Q2

14 marks Easy -1.3

2 The number of MPs in the House of Commons was 645 at the beginning of August 2009. The genders of these MPs and the political parties to which they belonged are shown in the table.

\multirow{2}{*}{}		Political Party
		Labour	Conservative	Liberal Democrat	Other	Total
\multirow{2}{*}{Gender}	Male	255	175	54	35	519
	Female	94	18	9	5	126
	Total	349	193	63	40	645

One MP was selected at random for an interview. Calculate, to three decimal places, the probability that the MP was:
1. a male Conservative;
2. a male;
3. a Liberal Democrat;
4. Labour, given that the MP was female;
5. male, given that the MP was not Labour.
Two female MPs were selected at random for an enquiry. Calculate, to three decimal places, the probability that both MPs were Labour.
Three MPs were selected at random for a committee. Calculate, to three decimal places, the probability that exactly one MP was Labour and exactly one MP was Conservative.

AQA S1 2011 January Q3

13 marks Moderate -0.3

3 The volume, $X$ litres, of orange juice in a 1-litre carton may be modelled by a normal distribution with unknown mean $\mu$. The volumes, $x$ litres, recorded to the nearest 0.01 litre, in a random sample of 100 cartons are shown in the table.

Volume ( $\boldsymbol { x }$ litres)	Number of cartons (f)
0.95-0.97	2
0.98-1.00	7
1.01-1.03	15
1.04-1.06	32
1.07-1.09	22
1.10-1.12	14
1.13-1.15	7
1.16-1.18	1
Total	100

For the group ' $0.98 - 1.00$ ':
1. show that it has a mid-point of 0.99 litres;
2. state the minimum and the maximum values of $x$ that could be included in this group.
Calculate, to three decimal places, estimates of the mean and the standard deviation of these 100 volumes.
1. Construct an approximate $99 \%$ confidence interval for $\mu$.
2. State why use of the Central Limit Theorem was not required when calculating this confidence interval.
3. Give a reason why the confidence interval is approximate rather than exact.
Give a reason in support of the claim that:
1. $\mu > 1$;
2. $\mathrm { P } ( 0.94 < X < 1.16 )$ is approximately 1 .
  \includegraphics[max width=\textwidth, alt={}]{156f9453-ebc6-4406-b5bc-08d1918ebc62-10_2486_1714_221_153}
  
  \includegraphics[max width=\textwidth, alt={}]{156f9453-ebc6-4406-b5bc-08d1918ebc62-11_2486_1714_221_153}

AQA S1 2011 January Q4

15 marks Moderate -0.3

4 Clay pigeon shooting is the sport of shooting at special flying clay targets with a shotgun.

Rhys, a novice, uses a single-barrelled shotgun. The probability that he hits a target is 0.45 , and may be assumed to be independent from target to target. Determine the probability that, in a series of shots at 15 targets, he hits:
1. at most 5 targets;
2. more than 10 targets;
3. exactly 6 targets;
4. at least 5 but at most 10 targets.
Sasha, an expert, uses a double-barrelled shotgun. She shoots at each target with the gun's first barrel and, only if she misses, does she then shoot at the target with the gun's second barrel. The probability that she hits a target with a shot using her gun's first barrel is 0.85 . The conditional probability that she hits a target with a shot using her gun's second barrel, given that she has missed the target with a shot using her gun's first barrel, is 0.80 . Assume that Sasha's shooting is independent from target to target.
1. Show that the probability that Sasha hits a target is 0.97 .
2. Determine the probability that, in a series of shots at 50 targets, Sasha hits at least 48 targets.
3. In a series of shots at 80 targets, calculate the mean number of times that Sasha shoots at targets with her gun's second barrel.
  \includegraphics[max width=\textwidth, alt={}]{156f9453-ebc6-4406-b5bc-08d1918ebc62-14_2486_1714_221_153}

AQA S1 2011 January Q5

14 marks Moderate -0.3

5 Craig uses his car to travel regularly from his home to the area hospital for treatment. He leaves home at $x$ minutes after 7.30 am and then takes $y$ minutes to arrive at the hospital's reception desk. His results for 11 mornings are shown in the table.

$\boldsymbol { x }$	0	5	10	15	20	25	30	35	40	45	50
$\boldsymbol { y }$	31	42	32	58	47	56	79	68	89	95	85

Explain why the time taken by Craig between leaving home and arriving at the hospital's reception desk is the response variable.
Calculate the equation of the least squares regression line of $y$ on $x$, writing your answer in the form $y = a + b x$.
On a particular day, Craig needs to arrive at the hospital's reception desk no later than 9.00 am . He leaves home at 7.45 am . Estimate the number of minutes before 9.00 am that Craig will arrive at the hospital's reception desk. Give your answer to the nearest minute.
1. Use your equation to estimate $y$ when $x = 85$.
2. Give one statistical reason and one reason based on the context of this question as to why your estimate in part (d)(i) is unlikely to be realistic.埗

AQA S1 2011 January Q6

12 marks Standard +0.8

6 The volume of shampoo, $V$ millilitres, delivered by a machine into bottles may be modelled by a normal random variable with mean $\mu$ and standard deviation $\sigma$.

Given that $\mu = 412$ and $\sigma = 8$, determine:
1. $\mathrm { P } ( V < 400 )$;
2. $\mathrm { P } ( V > 420 )$;
3. $\mathrm { P } ( V = 410 )$.
A new quality control specification requires that the values of $\mu$ and $\sigma$ are changed so that $$\mathrm { P } ( V < 400 ) = 0.05 \quad \text { and } \quad \mathrm { P } ( V > 420 ) = 0.01$$
1. Show, with the aid of a suitable sketch, or otherwise, that $$400 - \mu = - 1.6449 \sigma \quad \text { and } \quad 420 - \mu = 2.3263 \sigma$$
2. Hence calculate values for $\mu$ and $\sigma$.

AQA S1 2012 January Q1

4 marks Easy -1.8

1 Giles, a keen gardener, rents a council allotment. During early April 2011, he planted 27 seed potatoes. When he harvested his potato crop during the following August, he counted the number of new potatoes that he obtained from each seed potato. He recorded his results as follows.

Number of new potatoes	$\leqslant 6$	7	8	9	10	11	$\geqslant 12$
Frequency	2	2	1	4	8	6	4

Calculate values for the median and the interquartile range of these data.
Advise Giles on how to record his corresponding data for 2012 so that it would then be possible to calculate the mean number of new potatoes per seed potato.

AQA S1 2012 January Q2

3 marks Moderate -0.8

2 Dr Hanna has a special clinic for her older patients. She asked a medical student, Lenny, to select a random sample of 25 of her male patients, aged between 55 and 65 years, and, from their clinical records, to list their heights, weights and waist measurements. Lenny was then asked to calculate three values of the product moment correlation coefficient based upon his collected data. His results were:

0.365 between height and waist measurement;
1.16 between height and weight;
- 0.583 between weight and waist measurement. For each of Lenny's three calculated values, state whether the value is definitely correct, probably correct, probably incorrect or definitely incorrect.

AQA S1 2012 January Q3

12 marks Moderate -0.8

3 During June 2011, the volume, $X$ litres, of unleaded petrol purchased per visit at a supermarket's filling station by private-car customers could be modelled by a normal distribution with a mean of 32 and a standard deviation of 10 .

Determine:
1. $\mathrm { P } ( X < 40 )$;
2. $\mathrm { P } ( X > 25 )$;
3. $\mathrm { P } ( 25 < X < 40 )$.
Given that during June 2011 unleaded petrol cost $\pounds 1.34$ per litre, calculate the probability that the unleaded petrol bill for a visit during June 2011 by a private-car customer exceeded $\pounds 65$.
Give two reasons, in context, why the model $\mathrm { N } \left( 32,10 ^ { 2 } \right)$ is unlikely to be valid for a visit by any customer purchasing fuel at this filling station during June 2011.
(2 marks)

AQA S1 2012 January Q4

14 marks Moderate -0.3

4 The records at a passport office show that, on average, 15 per cent of photographs that accompany applications for passport renewals are unusable. Assume that exactly one photograph accompanies each application.

Determine the probability that in a random sample of 40 applications:
1. exactly 6 photographs are unusable;
2. at most 5 photographs are unusable;
3. more than 5 but fewer than 10 photographs are unusable.
Calculate the mean and the standard deviation for the number of photographs that are unusable in a random sample of $\mathbf { 3 2 }$ applications.
Mr Stickler processes 32 applications each day. His records for the previous 10 days show that the numbers of photographs that he deemed unusable were $$\begin{array} { l l l l l l l l l l } 8 & 6 & 10 & 7 & 9 & 7 & 8 & 9 & 6 & 7 \end{array}$$ By calculating the mean and the standard deviation of these values, comment, with reasons, on the suitability of the $\mathrm { B } ( 32,0.15 )$ model for the number of photographs deemed unusable each day by Mr Stickler.

AQA S1 2012 January Q5

17 marks Moderate -0.8

5 An experiment was undertaken to collect information on the burning of a specific type of wood as a source of energy. At given fixed levels of the wood's moisture content, $x$ per cent, its corresponding calorific value, $y \mathrm { MWh } /$ tonne, on burning was determined. The results are shown in the table.

$\boldsymbol { x }$	5	10	15	20	25	30	35	40	45	50	55	60	65
$\boldsymbol { y }$	5.2	4.7	4.3	4.0	3.2	2.8	2.5	2.2	1.8	1.5	1.3	1.0	0.6

Explain why calorific value is the response variable.
Calculate the equation of the least squares regression line of $y$ on $x$, giving your answer in the form $y = a + b x$.
Interpret, in context, your values for $a$ and $b$.
Use your equation to estimate the wood's calorific value when it has a moisture content of 27 per cent.
Calculate the value of the residual for the point $( 35,2.5 )$.
Given that the values of the 13 residuals lie between - 0.28 and + 0.23 , comment on the likely accuracy of your estimate in part (d).
1. Give a general reason why your equation should not be used to estimate the wood's calorific value when it has a moisture content of 80 per cent.
2. Give a specific reason, based on the context of this question and with numerical support, why your equation cannot be used to estimate the wood's calorific value when it has a moisture content of 80 per cent.

AQA S1 2012 January Q6

11 marks Moderate -0.8

6 Twins Alec and Eric are members of the same local cricket club and play for the club’s under 18 team. The probability that Alec is selected to play in any particular game is 0.85 .
The probability that Eric is selected to play in any particular game is 0.60 .
The probability that both Alec and Eric are selected to play in any particular game is 0.55 .

By using a table, or otherwise:
1. show that the probability that neither twin is selected for a particular game is 0.10 ;
2. find the probability that at least one of the twins is selected for a particular game;
3. find the probability that exactly one of the twins is selected for a particular game.
The probability that the twins' younger brother, Cedric, is selected for a particular game is:
0.30 given that both of the twins have been selected;
0.75 given that exactly one of the twins has been selected;
0.40 given that neither of the twins has been selected. Calculate the probability that, for a particular game:
1. all three brothers are selected;
2. at least two of the three brothers are selected.
  (6 marks)

AQA S1 2012 January Q7

14 marks Standard +0.3

7 A random sample of 50 full-time university employees was selected as part of a higher education salary survey. The annual salary in thousands of pounds, $x$, of each employee was recorded, with the following summarised results. $$\sum x = 2290.0 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 28225.50$$ Also recorded was the fact that 6 of the 50 salaries exceeded $\pounds 60000$.

1. Calculate values for $\bar { x }$ and $s$, where $s ^ { 2 }$ denotes the unbiased estimate of $\sigma ^ { 2 }$.
2. Hence show why the annual salary, $X$, of a full-time university employee is unlikely to be normally distributed. Give numerical support for your answer.
1. Indicate why the mean annual salary, $\bar { X }$, of a random sample of 50 full-time university employees may be assumed to be normally distributed.
2. Hence construct a $99 \%$ confidence interval for the mean annual salary of full-time university employees.
It is claimed that the annual salaries of full-time university employees have an average which exceeds $\pounds 55000$ and that more than $25 \%$ of such salaries exceed £60000. Comment on each of these two claims.

AQA S1 2013 January Q1

9 marks Moderate -0.8

1 Bob, a church warden, decides to investigate the lifetime of a particular manufacturer's brand of beeswax candle. Each candle is 30 cm in length. From a box containing a large number of such candles, he selects one candle at random. He lights the candle and, after it has burned continuously for $x$ hours, he records its length, $y \mathrm {~cm}$, to the nearest centimetre. His results are shown in the table.

$\boldsymbol { x }$	5	10	15	20	25	30	35	40	45
$\boldsymbol { y }$	27	25	21	19	16	11	9	5	2

State the value that you would expect for $a$ in the equation of the least squares regression line, $y = a + b x$.
1. Calculate the equation of the least squares regression line, $y = a + b x$.
2. Interpret the value that you obtain for $b$.
3. It is claimed by the candle manufacturer that the total length of time that such candles are likely to burn for is more than 50 hours. Comment on this claim, giving a numerical justification for your answer.

AQA S1 2013 January Q2

9 marks Moderate -0.8

2 The volume of Everwhite toothpaste in a pump-action dispenser may be modelled by a normal distribution with a mean of 106 ml and a standard deviation of 2.5 ml . Determine the probability that the volume of Everwhite in a randomly selected dispenser is:

less than 110 ml ;
more than 100 ml ;
between 104 ml and 108 ml ;
not exactly 106 ml .

AQA S1 2013 January Q3

14 marks Moderate -0.3

3 Stopoff owns a chain of hotels. Guests are presented with the bills for their stays when they check out.

Assume that the number of bills that contain errors may be modelled by a binomial distribution with parameters $n$ and $p$, where $p = 0.30$. Determine the probability that, in a random sample of 40 bills:
1. at most 10 bills contain errors;
2. at least 15 bills contain errors;
3. exactly 12 bills contain errors.
Calculate the mean and the variance for each of the distributions $\mathrm { B } ( 16,0.20 )$ and $B ( 16,0.125 )$.
Stan, who is a travelling salesperson, always uses Stopoff hotels. He holds one of its diamond customer cards and so should qualify for special customer care. However, he regularly finds errors in his bills when he checks out. Each month, during a 12-month period, Stan stayed in Stopoff hotels on exactly 16 occasions. He recorded, each month, the number of occasions on which his bill contained errors. His recorded values were as follows. $$\begin{array} { l l l l l l l l l l l l } 2 & 1 & 4 & 3 & 1 & 3 & 0 & 3 & 1 & 0 & 5 & 1 \end{array}$$
1. Calculate the mean and the variance of these 12 values.
2. Hence state with reasons which, if either, of the distributions $\mathrm { B } ( 16,0.20 )$ and $B ( 16,0.125 )$ is likely to provide a satisfactory model for these 12 values.

AQA S1 2013 January Q4

12 marks Moderate -0.3

4 Ashok is a work-experience student with an organisation that offers two separate professional examination papers, I and II. For each of a random sample of 12 students, A to L , he records the mark, $x$ per cent, achieved on Paper I, and the mark, $y$ per cent, achieved on Paper II.

\cline { 2 - 13 } \multicolumn{1}{c\|}{}	$\mathbf { A }$	$\mathbf { B }$	$\mathbf { C }$	$\mathbf { D }$	$\mathbf { E }$	$\mathbf { F }$	$\mathbf { G }$	$\mathbf { H }$	$\mathbf { I }$	$\mathbf { J }$	$\mathbf { K }$	$\mathbf { L }$
$\boldsymbol { x }$	34	46	53	62	67	72	60	54	70	71	82	85
$\boldsymbol { y }$	61	66	72	78	88	81	49	60	54	44	49	36

1. Calculate the value of the product moment correlation coefficient, $r$, between $x$ and $y$.
2. Interpret your value of $r$ in the context of this question.
1. Give two possible advantages of plotting data on a graph before calculating the value of a product moment correlation coefficient.
2. Complete the plotting of Ashok's data on the scatter diagram on page 5.
3. State what is now revealed by the scatter diagram.

Ashok subsequently discovers that students A to F have a more scientific background than students G to L. With reference to your scatter diagram, estimate the value of the product moment correlation coefficient for each of the two groups of students. You are not expected to calculate the two values.

\cline { 2 - 7 } \multicolumn{1}{c\|}{}	$\mathbf { G }$	$\mathbf { H }$	$\mathbf { I }$	$\mathbf { J }$	$\mathbf { K }$	$\mathbf { L }$
$\boldsymbol { x }$	60	54	70	71	82	85
$\boldsymbol { y }$	49	60	54	44	49	36

\section*{Examination Marks}

\includegraphics[max width=\textwidth, alt={}]{68830a6a-5479-4e5c-a845-a6536ab51cee-5_1616_1634_836_189}

AQA S1 2013 January Q5

12 marks Easy -1.3

5 Roger is an active retired lecturer. Each day after breakfast, he decides whether the weather for that day is going to be fine ( $F$ ), dull ( $D$ ) or wet ( $W$ ). He then decides on only one of four activities for the day: cycling ( $C$ ), gardening ( $G$ ), shopping ( $S$ ) or relaxing $( R )$. His decisions from day to day may be assumed to be independent. The table shows Roger's probabilities for each combination of weather and activity.

\multirow{2}{*}{}		Weather
		Fine ( $F$ )	Dull ( $D$ )	Wet ( $\boldsymbol { W }$ )
\multirow{4}{*}{Activity}	Cycling ( $\boldsymbol { C }$ )	0.30	0.10	0
	Gardening ( $\boldsymbol { G }$ )	0.25	0.05	0
	Shopping ( $\boldsymbol { S }$ )	0	0.10	0.05
	Relaxing ( $\boldsymbol { R }$ )	0	0.05	0.10

Find the probability that, on a particular day, Roger decided:
1. that it was going to be fine and that he would go cycling;
2. on either gardening or shopping;
3. to go cycling, given that he had decided that it was going to be fine;
4. not to relax, given that he had decided that it was going to be dull;
5. that it was going to be fine, given that he did not go cycling.
Calculate the probability that, on a particular Saturday and Sunday, Roger decided that it was going to be fine and decided on the same activity for both days.

AQA S1 2013 January Q6

10 marks Moderate -0.3

The length of one-metre galvanised-steel straps used in house building may be modelled by a normal distribution with a mean of 1005 mm and a standard deviation of 15 mm . The straps are supplied to house builders in packs of 12, and the straps in a pack may be assumed to be a random sample. Determine the probability that the mean length of straps in a pack is less than one metre.
Tania, a purchasing officer for a nationwide house builder, measures the thickness, $x$ millimetres, of each of a random sample of 24 galvanised-steel straps supplied by a manufacturer. She then calculates correctly that the value of $\bar { x }$ is 4.65 mm .
1. Assuming that the thickness, $X \mathrm {~mm}$, of such a strap may be modelled by the distribution $\mathrm { N } \left( \mu , 0.15 ^ { 2 } \right)$, construct a $99 \%$ confidence interval for $\mu$.
2. Hence comment on the manufacturer's specification that the mean thickness of such straps is greater than 4.5 mm .

AQA S1 2013 January Q7

9 marks Standard +0.3

7 A machine, which cuts bread dough for loaves, can be adjusted to cut dough to any specified set weight. For any set weight, $\mu$ grams, the actual weights of cut dough are known to be approximately normally distributed with a mean of $\mu$ grams and a fixed standard deviation of $\sigma$ grams. It is also known that the machine cuts dough to within 10 grams of any set weight.

Estimate, with justification, a value for $\sigma$.
The machine is set to cut dough to a weight of 415 grams. As a training exercise, Sunita, the quality control manager, asked Dev, a recently employed trainee, to record the weight of each of a random sample of 15 such pieces of dough selected from the machine's output. She then asked him to calculate the mean and the standard deviation of his 15 recorded weights. Dev subsequently reported to Sunita that, for his sample, the mean was 391 grams and the standard deviation was 95.5 grams. Advise Sunita on whether or not each of Dev's values is likely to be correct. Give numerical support for your answers.
Maria, an experienced quality control officer, recorded the weight, $y$ grams, of each of a random sample of 10 pieces of dough selected from the machine's output when it was set to cut dough to a weight of 820 grams. Her summarised results were as follows. $$\sum y = 8210.0 \quad \text { and } \quad \sum ( y - \bar { y } ) ^ { 2 } = 110.00$$ Explain, with numerical justifications, why both of these values are likely to be correct.

AQA S1 2007 June Q1

5 marks Moderate -0.8

1 The table shows the length, in centimetres, and maximum diameter, in centimetres, of each of 10 honeydew melons selected at random from those on display at a market stall.

Length	24	25	19	28	27	21	35	23	32	26
Maximum diameter	18	14	16	11	13	14	12	16	15	14

Calculate the value of the product moment correlation coefficient.
Interpret your value in the context of this question.

Patient	\(\mathbf { A }\)	\(\mathbf { B }\)	\(\mathbf { C }\)	\(\mathbf { D }\)	\(\mathbf { E }\)	\(\mathbf { F }\)	\(\mathbf { G }\)	\(\mathbf { H }\)	\(\mathbf { I }\)	\(\mathbf { J }\)
\(\boldsymbol { x }\)	55	51	62	66	72	59	78	55	62	70
\(\boldsymbol { y }\)	34	33	39	49	48	43	51	41	46	51

\(\boldsymbol { x }\)	22.5	22.7	22.6	22.4	22.5	22.8	22.6	22.7	22.8	22.4	22.9	22.6
\(\boldsymbol { y }\)	160.3	159.4	157.8	158.0	157.3	159.8	158.3	159.6	161.3	156.4	162.5	161.2

Volume ( \(\boldsymbol { x }\) litres)	Number of cartons (f)
0.95-0.97	2
0.98-1.00	7
1.01-1.03	15
1.04-1.06	32
1.07-1.09	22
1.10-1.12	14
1.13-1.15	7
1.16-1.18	1
Total	100

Number of new potatoes	\(\leqslant 6\)	7	8	9	10	11	\(\geqslant 12\)
Frequency	2	2	1	4	8	6	4

\multirow{2}{*}{}		Weather
		Fine ( \(F\) )	Dull ( \(D\) )	Wet ( \(\boldsymbol { W }\) )
\multirow{4}{*}{Activity}	Cycling ( \(\boldsymbol { C }\) )	0.30	0.10	0
	Gardening ( \(\boldsymbol { G }\) )	0.25	0.05	0
	Shopping ( \(\boldsymbol { S }\) )	0	0.10	0.05
	Relaxing ( \(\boldsymbol { R }\) )	0	0.05	0.10

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AQA S1 2013 January Q1

AQA S1 2013 January Q2

AQA S1 2013 January Q3

AQA S1 2013 January Q4

AQA S1 2013 January Q5

AQA S1 2013 January Q6

AQA S1 2013 January Q7

AQA S1 2007 June Q1