Questions S1 (2020 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 S1 S2 S3 S4 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 PURE S1 S2 S3 S4 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 Pre-U Pre-U 9794/1 Pre-U 9794/2 Pre-U 9794/3 Pre-U 9795 Pre-U 9795/1 Pre-U 9795/2 WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
Sort by: Default | Easiest first | Hardest first
AQA S1 2014 June Q4
10 marks Easy -1.3
4 Alf and Mabel are members of a bowls club and sometimes attend the club's social events. The probability, \(\mathrm { P } ( A )\), that Alf attends a social event is 0.70 .
The probability, \(\mathrm { P } ( M )\), that Mabel attends a social event is 0.55 .
The probability, \(\mathrm { P } ( A \cap M )\), that both Alf and Mabel attend the same social event is 0.45 .
  1. Find the probability that:
    1. either Alf or Mabel or both attend a particular social event;
    2. either Alf or Mabel but not both attend a particular social event.
  2. Give a numerical justification for the following statement.
    "Events \(A\) and \(M\) are not independent."
  3. Ben and Nora are also members of the bowls club and sometimes attend the club's social events. The probability, \(\mathrm { P } ( B )\), that Ben attends a social event is 0.85 .
    The probability, \(\mathrm { P } ( N )\), that Nora attends a social event is 0.65 .
    The attendance of each of Ben and Nora at a social event is independent of the attendance of all other members. Find the probability that:
    1. all four named members attend a particular social event;
    2. none of the four named members attend a particular social event.
AQA S1 2014 June Q5
13 marks Moderate -0.5
5 As part of a study of charity shops in a small market town, two such shops, \(X\) and \(Y\), were each asked to provide details of its takings on 12 randomly selected days. The table shows, for each of the 12 days, the day's takings, \(\pounds x\), of charity shop \(X\) and the day's takings, \(\pounds y\), of charity shop \(Y\).
Day\(\mathbf { A }\)\(\mathbf { B }\)\(\mathbf { C }\)\(\mathbf { D }\)\(\mathbf { E }\)\(\mathbf { F }\)\(\mathbf { G }\)\(\mathbf { H }\)\(\mathbf { I }\)\(\mathbf { J }\)\(\mathbf { K }\)\(\mathbf { L }\)
\(\boldsymbol { x }\)4657391166277416115536861
\(\boldsymbol { y }\)781026621498729813421679583
    1. Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
    2. Interpret your value in the context of this question.
  2. Complete the scatter diagram shown on the opposite page.
  3. The investigator realised subsequently that one of the 12 selected days was a particularly popular town market day and another was a day on which the weather was extremely severe. Identify each of these days giving a reason for each choice.
  4. Removing the two days described in part (c) from the data gives the following information. $$S _ { x x } = 1292.5 \quad S _ { y y } = 3850.1 \quad S _ { x y } = 407.5$$
    1. Use this information to recalculate the value of the product moment correlation coefficient between \(x\) and \(y\).
    2. Hence revise, as necessary, your interpretation in part (a)(ii).
      [0pt] [3 marks] Shop \(X\) takings(£) \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{harity Shops} \includegraphics[alt={},max width=\textwidth]{ddf7f158-b6ae-42c6-98f1-d59c205646ad-17_33_21_294_1617}
      \end{figure} \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{harity Shops} \includegraphics[alt={},max width=\textwidth]{ddf7f158-b6ae-42c6-98f1-d59c205646ad-17_49_24_276_1710}
      \end{figure}
      \includegraphics[max width=\textwidth, alt={}]{ddf7f158-b6ae-42c6-98f1-d59c205646ad-17_1304_415_406_1391}
      レ
AQA S1 2014 June Q6
14 marks Moderate -0.3
6 The probability that an online order from a supermarket chain has at least one item missing when delivered is 0.06 . Online orders are 'incomplete' if they contain substitute items and/or have at least one item missing when delivered. The probability that an order is incomplete is 0.15 .
  1. Calculate the probability that exactly 2 out of a random sample of 26 online orders have at least one item missing when delivered.
  2. Determine the probability that the number of incomplete orders in a random sample of 50 online orders is:
    1. fewer than 10 ;
    2. more than 5;
    3. more than 6 but fewer than 12 .
  3. Farokh, the manager of one of the supermarket's stores, examines 50 randomly selected online orders from each of a random sample of 100 of the store's customers. He records, for each of the 50 orders, the number, \(x\), that were incomplete. His summarised results, correct to three significant figures, for the 100 customers selected are $$\bar { x } = 4.33 \text { and } s ^ { 2 } = 3.94$$ Use this information to compare the performance of the store managed by Farokh with that of the supermarket chain as a whole.
    [0pt] [5 marks]
AQA S1 2014 June Q7
11 marks Moderate -0.3
7 For the year 2014, the table below summarises the weights, \(x\) kilograms, of a random sample of 160 women residing in a particular city who are aged between 18 years and 25 years.
Weight ( \(\boldsymbol { x }\) kg)Number of women
35-404
40-459
45-5012
50-5516
55-6024
60-6528
65-7024
70-7517
75-8012
80-857
85-904
90-952
95-1001
Total160
  1. Calculate estimates of the mean and the standard deviation of these 160 weights.
    1. Construct a 98\% confidence interval for the mean weight of women residing in the city who are aged between 18 years and 25 years.
    2. Hence comment on a claim that the mean weight of women residing in the city who are aged between 18 years and 25 years has increased from that of 61.7 kg in 1965.
      [0pt] [2 marks]
      \includegraphics[max width=\textwidth, alt={}]{ddf7f158-b6ae-42c6-98f1-d59c205646ad-28_2488_1728_219_141}
AQA S1 2014 June Q1
11 marks Easy -1.3
1 Henrietta lives on a small farm where she keeps some hens.
For a period of 35 weeks during the hens' first laying season, she records, each week, the total number of eggs laid by the hens. Her records are shown in the table.
Total number of eggs laid in a week ( \(\boldsymbol { x }\) )Number of weeks ( f)
661
672
683
695
707
718
724
732
742
751
Total35
  1. For these data:
    1. state values for the mode and the range;
    2. find values for the median and the interquartile range;
    3. calculate values for the mean and the standard deviation.
  2. Each week, for the 35 weeks, Henrietta sells 60 eggs to a local shop, keeping the remainder for her own use. State values for the mean and the standard deviation of the number of eggs that she keeps.
    [0pt] [2 marks]
AQA S1 2014 June Q2
10 marks Moderate -0.8
2 A garden centre sells bamboo canes of nominal length 1.8 metres. The length, \(X\) metres, of the canes can be modelled by a normal distribution with mean 1.86 and standard deviation \(\sigma\).
  1. Assuming that \(\sigma = 0.04\), determine:
    1. \(\mathrm { P } ( X < 1.90 )\);
    2. \(\mathrm { P } ( X > 1.80 )\);
    3. \(\mathrm { P } ( 1.80 < X < 1.90 )\);
    4. \(\mathrm { P } ( X \neq 1.86 )\).
  2. It is subsequently found that \(\mathrm { P } ( X > 1.80 ) = 0.98\). Determine the value of \(\sigma\).
    [0pt] [3 marks]
    \includegraphics[max width=\textwidth, alt={}]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-06_1529_1717_1178_150}
AQA S1 2014 June Q3
12 marks Easy -1.2
3 The table shows the colour of hair and the colour of eyes of a sample of 750 people from a particular population.
AQA S1 2014 June Q4
7 marks Moderate -0.3
4 Every year, usually during early June, the Isle of Man hosts motorbike races. Each race consists of three consecutive laps of the island's course. To compete in a race, a rider must first complete at least one qualifying lap. The data refer to the lightweight motorbike class in 2012 and show, for each of a random sample of 10 riders, values of $$u = x - 100 \quad \text { and } \quad v = y - 100$$ where \(x\) denotes the average speed, in mph, for the rider's fastest qualifying lap and \(y\) denotes the average speed, in mph, for the rider's three laps of the race.
\cline { 2 - 11 } \multicolumn{1}{c|}{}Rider
\cline { 2 - 11 } \multicolumn{1}{c|}{}\(\mathbf { A }\)\(\mathbf { B }\)\(\mathbf { C }\)\(\mathbf { D }\)\(\mathbf { E }\)\(\mathbf { F }\)\(\mathbf { G }\)\(\mathbf { H }\)\(\mathbf { I }\)\(\mathbf { J }\)
\(\boldsymbol { u }\)7.8813.024.292.886.267.033.6011.7813.1511.69
\(\boldsymbol { v }\)6.6310.163.630.475.708.013.307.3113.0811.82
    1. Calculate the value of \(r _ { u v }\), the product moment correlation coefficient between \(u\) and \(v\).
    2. Hence state the value of \(r _ { x y }\), giving a reason for your answer.
  2. Interpret your value of \(r _ { x y }\) in the context of this question.
AQA S1 2014 June Q5
13 marks Moderate -0.3
5 An analysis of the number of vehicles registered by each household within a city resulted in the following information.
Number of vehicles registered012\(\geqslant 3\)
Percentage of households18472510
  1. A random sample of 30 households within the city is selected. Use a binomial distribution with \(n = 30\), together with relevant information from the table in each case, to find the probability that the sample contains:
    1. exactly 3 households with no registered vehicles;
    2. at most 5 households with three or more registered vehicles;
    3. more than 10 households with at least two registered vehicles;
    4. more than 5 households but fewer than 10 households with exactly two registered vehicles.
  2. If a random sample of \(\mathbf { 1 5 0 }\) households within the city were to be selected, estimate the mean and the variance for the number of households in the sample that would have either one or two registered vehicles.
    [0pt] [2 marks]
    \includegraphics[max width=\textwidth, alt={}]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-16_1075_1707_1628_153}
AQA S1 2014 June Q6
12 marks Moderate -0.8
6 A rubber seal is fitted to the bottom of a flood barrier. When no pressure is applied, the depth of the seal is 15 cm . When pressure is applied, a watertight seal is created between the flood barrier and the ground. The table shows the pressure, \(x\) kilopascals ( kPa ), applied to the seal and the resultant depth, \(y\) centimetres, of the seal.
\(\boldsymbol { x }\)255075100125150175200250300
\(\boldsymbol { y }\)14.713.412.811.911.010.39.79.07.56.7
    1. State the value that you would expect for \(a\) in the equation of the least squares regression line, \(y = a + b x\).
    2. Calculate the equation of the least squares regression line, \(y = a + b x\).
    3. Interpret, in context, your value for \(b\).
  2. Calculate an estimate of the depth of the seal when it is subjected to a pressure of 225 kPa .
    1. Give a statistical reason as to why your equation is unlikely to give a realistic estimate of the depth of the seal if it were to be subjected to a pressure of 400 kPa .
    2. Give a reason based on the context of this question as to why your equation will not give a realistic estimate of the depth of the seal if it were to be subjected to a pressure of 525 kPa .
      [0pt] [3 marks]
      \includegraphics[max width=\textwidth, alt={}]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-20_946_1709_1761_153}
      \includegraphics[max width=\textwidth, alt={}]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-21_2484_1707_221_153}
      \includegraphics[max width=\textwidth, alt={}]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-23_2484_1707_221_153}
AQA S1 2014 June Q7
10 marks Moderate -0.3
7 The volume of water, \(V\), used by a guest in an en suite shower room at a small guest house may be modelled by a random variable with mean \(\mu\) litres and standard deviation 65 litres. A random sample of 80 guests using this shower room showed a mean usage of 118 litres of water.
    1. Give a numerical justification as to why \(V\) is unlikely to be normally distributed.
    2. Explain why \(\bar { V }\), the mean of a random sample of 80 observations of \(V\), may be assumed to be approximately normally distributed.
    1. Construct a \(98 \%\) confidence interval for \(\mu\).
    2. Hence comment on a claim that \(\mu\) is 140 .
      \includegraphics[max width=\textwidth, alt={}]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-24_1526_1709_1181_153}
      \includegraphics[max width=\textwidth, alt={}]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-25_2484_1707_221_153}
      \includegraphics[max width=\textwidth, alt={}, center]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-27_2490_1719_217_150} \includegraphics[max width=\textwidth, alt={}, center]{8aeacd54-a5a1-4f2d-b936-2faf635ffce7-28_2486_1728_221_141}
AQA S1 2016 June Q1
5 marks Moderate -0.8
1 The table shows the heights, \(x \mathrm {~cm}\), and the arm spans, \(y \mathrm {~cm}\), of a random sample of 12 men aged between 21 years and 40 years.
\(\boldsymbol { x }\)152166154159179167155168174182161163
\(\boldsymbol { y }\)143154151153168160146163170175155158
  1. Calculate the value of the product moment correlation coefficient between \(x\) and \(y\).
  2. Interpret, in context, your value calculated in part (a).
AQA S1 2016 June Q2
8 marks Moderate -0.8
2 A small chapel was open to visitors for 55 days during the summer of 2015. The table summarises the daily numbers of visitors.
Number of visitorsNumber of days
20 or fewer1
212
223
236
248
2510
2613
277
282
291
30 or more2
Total55
  1. For these data:
    1. state the modal value;
    2. find values for the median and the interquartile range.
  2. Name one measure of average and one measure of spread that cannot be calculated exactly from the data in the table.
    [0pt] [2 marks]
  3. Reference to the raw data revealed that the 3 unknown exact values in the table were 13,37 and 58. Making use of this additional information, together with the data in the table, calculate the value of each of the two measures that you named in part (b).
    [0pt] [3 marks]
AQA S1 2016 June Q3
14 marks Easy -1.2
3 The table shows, for a random sample of 500 patients attending a dental surgery, the patients' ages, in years, and the NHS charge bands for the patients' courses of treatment. Band 0 denotes the least expensive charge band and band 3 denotes the most expensive charge band.
\multirow{2}{*}{}Charge band for course of treatment
Band 0Band 1Band 2Band 3Total
\multirow{4}{*}{Age of patient (years)}Under 1932435080
Between 19 and 401762223104
Between 41 and 6528823531176
66 or over1353686140
Total9024013040500
  1. Calculate, to three decimal places, the probability that a patient, selected at random from these 500 patients, was:
    1. aged between 41 and 65;
    2. aged 66 or over and charged at band 2;
    3. aged between 19 and 40 and charged at most at band 1;
    4. aged 41 or over, given that the patient was charged at band 2;
    5. charged at least at band 2, given that the patient was not aged 66 or over.
  2. Four patients at this dental surgery, not included in the above 500 patients, are selected at random. Estimate, to three significant figures, the probability that two of these four patients are aged between 41 and 65 and are not charged at band 0 , and the other two patients are aged 66 or over and are charged at either band 1 or band 2.
    [0pt] [5 marks]
AQA S1 2016 June Q4
9 marks Moderate -0.8
4 As part of her science project, a student found the mass, \(y\) grams, of a particular compound that dissolved in 100 ml of water at each of 12 different set temperatures, \(x ^ { \circ } \mathrm { C }\). The results are shown in the table.
\(\boldsymbol { x }\)202530354045505560657075
\(\boldsymbol { y }\)242262269290298310326355359375390412
  1. Calculate the equation of the least squares regression line of \(y\) on \(x\).
  2. Interpret, in context, your value for the gradient of this regression line.
  3. Use your equation to estimate the mass of the compound which will dissolve in 100 ml of water at \(68 ^ { \circ } \mathrm { C }\).
  4. Given that the values of the 12 residuals for the regression line of \(y\) on \(x\) lie between - 7 and + 9 , comment, with justification, on the likely accuracy of your estimate in part (c).
    [0pt] [2 marks]
AQA S1 2016 June Q5
18 marks Moderate -0.3
5 Still mineral water is supplied in 1.5-litre bottles. The actual volume, \(X\) millilitres, in a bottle may be modelled by a normal distribution with mean \(\mu = 1525\) and standard deviation \(\sigma = 9.6\).
  1. Determine the probability that the volume of water in a randomly selected bottle is:
    1. less than 1540 ml ;
    2. more than 1535 ml ;
    3. between 1515 ml and 1540 ml ;
    4. not 1500 ml .
  2. The supplier requires that only 10 per cent of bottles should contain more than 1535 ml of water. Assuming that there has been no change in the value of \(\sigma\), calculate the reduction in the value of \(\mu\) in order to satisfy this requirement. Give your answer to one decimal place.
  3. Sparkling spring water is supplied in packs of six 0.5 -litre bottles. The actual volume in a bottle may be modelled by a normal distribution with mean 508.5 ml and standard deviation 3.5 ml . Stating a necessary assumption, determine the probability that:
    1. the volume of water in each of the 6 bottles from a randomly selected pack is more than 505 ml ;
    2. the mean volume of water in the 6 bottles from a randomly selected pack is more than 505 ml .
      [0pt] [7 marks]
AQA S1 2016 June Q6
12 marks Moderate -0.8
6 The proportions of different colours of loom bands in a box of 10000 loom bands are given in the table.
ColourBlueGreenRedOrangeYellowWhite
Proportion0.250.250.180.120.150.05
  1. A sample of 50 loom bands is selected at random from the box. Use a binomial distribution with \(n = 50\), together with relevant information from the table, to estimate the probability that this sample contains:
    1. exactly 4 red loom bands;
    2. at most 10 yellow loom bands;
    3. at least 30 blue or green loom bands;
    4. more than 35 but fewer than 45 loom bands that are neither yellow nor white.
  2. The random variable \(R\) denotes the number of red loom bands in a random sample of \(\mathbf { 3 0 0 }\) loom bands selected from the box. Estimate values for the mean and the variance of \(R\).
    [0pt] [2 marks]
AQA S1 2016 June Q7
9 marks Standard +0.3
7 Customers buying euros ( €) at a travel agency must pay for them in pounds ( \(\pounds\) ). The amounts paid, \(\pounds x\), by a sample of 40 customers were, in ascending order, as follows.
Edexcel S1 Q1
7 marks Moderate -0.8
  1. A histogram is to be drawn to represent the following grouped continuous data:
Group\(0 - 10\)\(10 - 20\)\(20 - 25\)\(25 - 30\)\(30 - 50\)\(50 - 100\)
Frequency\(2 x\)\(3 x\)\(5 x\)\(6 x\)\(2 x\)\(x\)
The ' \(10 - 20\) ' bar has height 6 cm and width 4 cm . Calculate
  1. the height of the ' \(20 - 25\) ' bar,
  2. the total area under the histogram.
Edexcel S1 Q2
7 marks Moderate -0.8
2. The events \(A\) and \(B\) are independent. Given that \(\mathrm { P } ( A ) = 0.4\) and \(\mathrm { P } ( A \cap B ) = 0.12\), find
  1. \(\mathrm { P } ( B )\),
  2. \(\mathrm { P } ( A \cup B )\),
  3. \(\mathrm { P } \left( A ^ { \prime } \cap B \right)\),
  4. \(\mathrm { P } \left( A \mid B ^ { \prime } \right)\).
Edexcel S1 Q3
9 marks Moderate -0.8
3. The random variable \(X\) has the discrete uniform distribution over the set of consecutive integers \(\{ - 7 , - 6 , \ldots , 10 \}\).
Calculate (a) the expectation and variance of \(X\),
(b) \(\mathrm { P } ( X > 7 )\),
(c) the value of \(n\) for which \(\mathrm { P } ( - n \leq X \leq n ) = \frac { 7 } { 18 }\).
Edexcel S1 Q4
9 marks Moderate -0.8
4. The marks, \(x\) out of 100 , scored by 30 candidates in an examination were as follows:
5192021232531373941
42444751565760616265
677071737577818298100
Given that \(\sum x = 1600\) and \(\sum x ^ { 2 } = 102400\),
  1. find the median, the mean and the standard deviation of these marks. The marks were scaled to give modified scores, \(y\), using the formula \(y = \frac { 4 x } { 5 } + 20\).
  2. Find the median, the mean and the standard deviation of the modified scores. \section*{STATISTICS 1 (A) TEST PAPER 1 Page 2}
Edexcel S1 Q5
12 marks Moderate -0.8
  1. The table shows the numbers of cars and vans in a company's fleet having registrations with the prefix letters shown.
Registration letter\(K\)\(L\)\(M\)\(N\)\(P\)\(R\)\(S\)\(T\)\(V\)
Number of cars \(( x )\)67911151412107
Number of vans \(( y )\)810141313151498
  1. Plot a scatter graph of this data, with the number of cars on the horizontal axis and the number of vans on the vertical axis.
  2. If there were \(4 J\)-registered cars, estimate the number of \(J\)-registered vans. Given that \(\sum x ^ { 2 } = 1001 , \sum y ^ { 2 } = 1264\) and \(\sum x y = 1106\),
  3. calculate the product-moment correlation coefficient between \(x\) and \(y\). Give a brief interpretation of your answer.
Edexcel S1 Q6
14 marks Moderate -0.3
6. The distributions of two independent discrete random variables \(X\) and \(Y\) are given in the tables:
\(x\)012
\(\mathrm { P } ( X = x )\)\(\frac { 3 } { 5 }\)\(\frac { 3 } { 10 }\)\(\frac { 1 } { 10 }\)
\(y\)01
\(\mathrm { P } ( Y = y )\)\(\frac { 5 } { 8 }\)\(\frac { 3 } { 8 }\)
The random variable \(Z\) is defined to be the sum of one observation from \(X\) and one from \(Y\).
  1. Tabulate the probability distribution for \(Z\).
  2. Calculate \(\mathrm { E } ( Z )\).
  3. Calculate (i) \(\mathrm { E } \left( Z ^ { 2 } \right)\), (ii) \(\operatorname { Var } ( Z )\).
  4. Calculate Var (3Z-4).
Edexcel S1 Q7
17 marks Standard +0.3
7. The times taken by a large number of people to read a certain book can be modelled by a normal distribution with mean \(5 \cdot 2\) hours. It is found that \(62 \cdot 5 \%\) of the people took more than \(4 \cdot 5\) hours to read the book.
  1. Show that the standard deviation of the times is approximately \(2 \cdot 2\) hours.
  2. Calculate the percentage of the people who took between 4 and 7 hours to read the book.
  3. Calculate the probability that two of the people chosen at random both took less than 5 hours to read the book, stating any assumption that you make.
  4. If a number of extra people were taken into account, all of whom took exactly \(5 \cdot 2\) hours to read the book, state with reasons what would happen to (i) the mean, (ii) the variance and explain briefly why the distribution would no longer be normal.