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
Edexcel S1 2017 October Q6
17 marks Moderate -0.3
  1. The discrete random variable \(D\) with the following probability distribution represents the score when a 4-sided die is rolled.
\(d\)1234
\(\mathrm { P } ( D = d )\)\(\frac { 1 } { 4 }\)\(\frac { 1 } { 4 }\)\(\frac { 1 } { 4 }\)\(\frac { 1 } { 4 }\)
  1. Write down the name of this distribution. The die is used to play a game and the random variable \(X\) represents the number of points scored. The die is rolled once and if \(D = 2,3\) or 4 then \(X = D\). If \(D = 1\) the die is rolled a second time and \(X = 0\) if \(D = 1\) again, otherwise \(X\) is the sum of the two scores on the die.
  2. Show that the probability of scoring 3 points in this game is \(\frac { 5 } { 16 }\)
  3. Find the probability of scoring 0 in this game. The table below shows the probability distribution for the remaining values of \(X\).
    \(x\)02345
    \(\mathrm { P } ( X = x )\)\(\frac { 1 } { 4 }\)\(\frac { 5 } { 16 }\)\(\frac { 1 } { 16 }\)
  4. Find \(\mathrm { E } ( X )\)
  5. Find \(\operatorname { Var } ( X )\) The discrete random variable \(R\) represents the number of times the die is rolled in the game.
  6. Write down the probability distribution of \(R\). The random variable \(Y = 2 R + 0.5\)
  7. Show that \(\mathrm { E } ( Y ) = \mathrm { E } ( X )\) The game is played once.
  8. Find \(\mathrm { P } ( X > Y )\)
Edexcel S1 2021 October Q1
7 marks Moderate -0.8
  1. The Venn diagram shows the events \(A\), \(B\) and \(C\) and their associated probabilities, where \(p\) and \(q\) are probabilities. \includegraphics[max width=\textwidth, alt={}, center]{29ac0c0b-f963-40a1-beba-7146bbb2d021-02_579_1054_347_447}
    1. Find \(\mathrm { P } ( B )\)
    2. Determine whether or not \(A\) and \(B\) are independent.
    Given that \(\mathrm { P } ( C \mid B ) = \mathrm { P } ( C )\)
  2. find the value of \(p\) and the value of \(q\) The event \(D\) is such that
    • \(\quad A\) and \(D\) are mutually exclusive
    • \(\mathrm { P } ( B \cap D ) > 0\)
    • On the Venn diagram show a possible position for the event \(D\)
Edexcel S1 2021 October Q2
12 marks Moderate -0.5
2. A large company is analysing how much money it spends on paper in its offices each year. The number of employees in the office, \(x\), and the amount spent on paper in a year, \(p\) (\$ hundreds), in each of 12 randomly selected offices were recorded. The results are summarised in the following statistics. $$\sum x = 93 \quad \mathrm {~S} _ { x x } = 148.25 \quad \sum p = 273 \quad \sum p ^ { 2 } = 6602.72 \quad \sum x p = 2347$$
  1. Show that \(\mathrm { S } _ { x p } = 231.25\)
  2. Find the product moment correlation coefficient for these data.
  3. Find the equation of the regression line of \(p\) on \(x\) in the form \(p = a + b x\)
  4. Give an interpretation of the gradient of your regression line. The director of the company wants to reduce the amount spent on paper each year. He wants each office to aim for a model of the form \(p = \frac { 4 } { 5 } a + \frac { 1 } { 2 } b x\), where \(a\) and \(b\) are the values found in part (c). Using the data for the 93 employees from the 12 offices,
  5. estimate the percentage saving in the amount spent on paper each year by the company using the director's model.
Edexcel S1 2021 October Q3
14 marks Moderate -0.8
  1. The stem and leaf diagram shows the ages of the 35 male passengers on a cruise.
Age
13\(( 1 )\)
279\(( 2 )\)
31288\(( 4 )\)
45567889\(( 7 )\)
52233445668\(( 10 )\)
60114447\(( 7 )\)
736\(( 2 )\)
878\(( 2 )\)
Key: 1 | 3 represents an age of 13 years
  1. Find the median age of the male passengers.
  2. Show that the interquartile range (IQR) of these ages is 16 An outlier is defined as a value that is more than \(1.5 \times\) IQR above the upper quartile
    or \(1.5 \times\) IQR below the lower quartile
  3. Show that there are 3 outliers amongst these ages.
  4. On the grid in Figure 1 on page 9, draw a box plot for the ages of the male passengers on the cruise. Figure 1 on page 9 also shows a box plot for the ages of the female passengers on the cruise.
  5. Comment on any difference in the distributions of ages of male and female passengers on the cruise.
    State the values of any statistics you have used to support your comment.
    (1) Anja, along with her 2 daughters and a granddaughter, now join the cruise.
    Anja's granddaughter is younger than both of Anja's daughters.
    Anja had her 23rd birthday on the day her eldest daughter was born.
    When their 4 ages are included with the other female passengers on the cruise, the box plot does not change.
  6. State, giving reasons, what you can say about
    1. the granddaughter's age
    2. Anja's age.
      (3)
      \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{29ac0c0b-f963-40a1-beba-7146bbb2d021-09_1025_1593_1541_182} \captionsetup{labelformat=empty} \caption{Figure 1}
      \end{figure}
Edexcel S1 2021 October Q4
13 marks Moderate -0.3
4. Three bags A, B and \(\mathbf { C }\) each contain coloured balls. Bag A contains 4 red balls and 2 yellow balls only.
Bag B contains 4 red balls and 1 yellow ball only.
Bag \(\mathbf { C }\) contains 6 red balls only. In a game
Mike takes a ball at random from bag \(\mathbf { A }\), records the colour and places it in bag \(\mathbf { C }\). He then takes a ball at random from bag \(\mathbf { B }\), records the colour and places it in bag \(\mathbf { C }\). Finally, Mike takes a ball at random from bag \(\mathbf { C }\) and records the colour.
  1. Complete the tree diagram on the page opposite, to illustrate the game by adding the remaining branches and all probabilities.
  2. Show that the probability that Mike records a yellow ball exactly twice is \(\frac { 1 } { 10 }\) Given that Mike records exactly 2 yellow balls,
  3. find the probability that the ball drawn from bag \(\mathbf { A }\) is red. Mike plays this game a large number of times, each time starting with the bags containing balls as described above. The random variable \(X\) represents the number of yellow balls recorded in a single game.
  4. Find the probability distribution of \(X\)
  5. Find \(\mathrm { E } ( X )\) Bag B
    Bag C \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Bag A} \includegraphics[alt={},max width=\textwidth]{29ac0c0b-f963-40a1-beba-7146bbb2d021-13_739_1580_411_182}
    \end{figure}
Edexcel S1 2021 October Q5
14 marks Standard +0.3
  1. The discrete random variable \(Y\) has the following probability distribution
\(y\)- 9- 5059
\(\mathrm { P } ( Y = y )\)\(q\)\(r\)\(u\)\(r\)\(q\)
where \(q , r\) and \(u\) are probabilities.
  1. Write down the value of \(\mathrm { E } ( Y )\) The cumulative distribution function of \(Y\) is \(\mathrm { F } ( y )\) Given that \(F ( 0 ) = \frac { 19 } { 30 }\)
  2. show that the value of \(u\) is \(\frac { 4 } { 15 }\) Given also that \(\operatorname { Var } ( Y ) = 37\)
  3. find the value of \(q\) and the value of \(r\) The coordinates of a point \(P\) are \(( 12 , Y )\) The random variable \(D\) represents the length of \(O P\)
  4. Find the probability distribution of \(D\)
Edexcel S1 2021 October Q6
15 marks Standard +0.3
  1. Xiang is designing shelves for a bookshop. The height, \(H \mathrm {~cm}\), of books is modelled by the normal distribution with mean 25.1 cm and standard deviation 5.5 cm
    1. Show that \(\mathrm { P } ( H > 30.8 ) = 0.15\)
    Xiang decided that the smallest \(5 \%\) of books and books taller than 30.8 cm would not be placed on the shelves. All the other books will be placed on the shelves.
  2. Find the range of heights of books that will be placed on the shelves.
    (3) The books that will be placed on the shelves have heights classified as small, medium or large.
    The numbers of small, medium and large books are in the ratios \(2 : 3 : 3\)
  3. The medium books have heights \(x \mathrm {~cm}\) where \(m < x < d\)
    1. Show that \(d = 25.8\) to 1 decimal place.
    2. Find the value of \(m\) Xiang wants 2 shelves for small books, 3 shelves for medium books and 3 shelves for large books.
      These shelves will be placed one above another and made of wood that is 1 cm thick.
  4. Work out the minimum total height needed.
Edexcel S1 Q1
Easy -1.2
  1. The students in a class were each asked to write down how many CDs they owned. The student with the least number of CDs had 14 and all but one of the others owned 60 or fewer. The remaining student owned 65 . The quartiles for the class were 30,34 and 42 respectively.
Outliers are defined to be any values outside the limits of \(1.5 \left( Q _ { 3 } - Q _ { 1 } \right)\) below the lower quartile or above the upper quartile. On graph paper draw a box plot to represent these data, indicating clearly any outliers.
(7 marks)
Edexcel S1 Q2
Moderate -0.8
2. The random variable \(X\) is normally distributed with mean 177.0 and standard deviation 6.4.
  1. Find \(\mathrm { P } ( 166 < X < 185 )\).
    (4 marks)
    It is suggested that \(X\) might be a suitable random variable to model the height, in cm , of adult males.
  2. Give two reasons why this is a sensible suggestion.
    (2 marks)
  3. Explain briefly why mathematical models can help to improve our understanding of real-world problems.
    (2 marks)
Edexcel S1 Q4
Easy -1.2
4. The employees of a company are classified as management, administration or production. The following table shows the number employed in each category and whether or not they live close to the company or some distance away.
Live close
Live some
distance away
Management614
Administration2510
Production4525
An employee is chosen at random.
Find the probability that this employee
  1. is an administrator,
  2. lives close to the company, given that the employee is a manager. Of the managers, \(90 \%\) are married, as are \(60 \%\) of the administrators and \(80 \%\) of the production employees.
  3. Construct a tree diagram containing all the probabilities.
  4. Find the probability that an employee chosen at random is married. (3 marks) An employee is selected at random and found to be married.
  5. Find the probability that this employee is in production.
Edexcel S1 Q5
Moderate -0.3
5. The following grouped frequency distribution summarises the number of minutes, to the nearest minute, that a random sample of 200 motorists were delayed by roadworks on a stretch of motorway.
Delay (mins)Number of motorists
\(4 - 6\)15
\(7 - 8\)28
949
1053
\(11 - 12\)30
\(13 - 15\)15
\(16 - 20\)10
  1. Using graph paper represent these data by a histogram.
  2. Give a reason to justify the use of a histogram to represent these data.
  3. Use interpolation to estimate the median of this distribution.
  4. Calculate an estimate of the mean and an estimate of the standard deviation of these data. One coefficient of skewness is given by $$\frac { 3 ( \text { mean } - \text { median } ) } { \text { standard deviation } } .$$
  5. Evaluate this coefficient for the above data.
  6. Explain why the normal distribution may not be suitable to model the number of minutes that motorists are delayed by these roadworks.
Edexcel S1 Q7
Moderate -0.8
7. A music teacher monitored the sight-reading ability of one of her pupils over a 10 week period. At the end of each week, the pupil was given a new piece to sight-read and the teacher noted the number of errors \(y\). She also recorded the number of hours \(x\) that the pupil had practised each week. The data are shown in the table below.
  1. Given that \(\mathrm { E } ( X ) = - 0.2\), find the value of \(\alpha\) and the value of \(\beta\).
  2. Write down \(\mathrm { F } ( 0.8 )\).
    1. Evaluate \(\operatorname { Var } ( X )\).
Edexcel S1 Q4
Easy -1.2
4. Aeroplanes fly from City \(A\) to City \(B\). Over a long period of time the number of minutes delay in take-off from City \(A\) was recorded. The minimum delay was 5 minutes and the maximum delay was 63 minutes. A quarter of all delays were at most 12 minutes, half were at most 17 minutes and \(75 \%\) were at most 28 minutes. Only one of the delays was longer than 45 minutes. An outlier is an observation that falls either \(1.5 \times\) (interquartile range) above the upper quartile or \(1.5 \times\) (interquartile range) below the lower quartile.
  1. On the graph paper opposite draw a box plot to represent these data.
  2. Comment on the distribution of delays. Justify your answer.
  3. Suggest how the distribution might be interpreted by a passenger who frequently flies from City \(A\) to City \(B\). \includegraphics[max width=\textwidth, alt={}, center]{3d4f7bfb-b235-418a-9411-a4d0b3188254-008_1190_1487_278_223}
Edexcel S1 Q7
Easy -1.8
7. In a school there are 148 students in Years 12 and 13 studying Science, Humanities or Arts subjects. Of these students, 89 wear glasses and the others do not. There are 30 Science students of whom 18 wear glasses. The corresponding figures for the Humanities students are 68 and 44 respectively. A student is chosen at random. Find the probability that this student
  1. is studying Arts subjects,
  2. does not wear glasses, given that the student is studying Arts subjects. Amongst the Science students, \(80 \%\) are right-handed. Corresponding percentages for Humanities and Arts students are 75\% and 70\% respectively. A student is again chosen at random.
  3. Find the probability that this student is right-handed.
  4. Given that this student is right-handed, find the probability that the student is studying Science subjects.
    1. (a) Describe the main features and uses of a box plot.
    Children from schools \(A\) and \(B\) took part in a fun run for charity. The times, to the nearest minute, taken by the children from school \(A\) are summarised in Figure 1. \begin{figure}[h]
    \captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{3d4f7bfb-b235-418a-9411-a4d0b3188254-015_398_1045_946_461}
    \end{figure}
    1. Write down the time by which \(75 \%\) of the children in school \(A\) had completed the run.
    2. State the name given to this value.
  6. Explain what you understand by the two crosses ( X ) on Figure 1.
Edexcel S1 Q8
Moderate -0.8
8. The lifetimes of bulbs used in a lamp are normally distributed. A company \(X\) sells bulbs with a mean lifetime of 850 hours and a standard deviation of 50 hours.
  1. Find the probability of a bulb, from company \(X\), having a lifetime of less than 830 hours.
  2. In a box of 500 bulbs, from company \(X\), find the expected number having a lifetime of less than 830 hours. A rival company \(Y\) sells bulbs with a mean lifetime of 860 hours and \(20 \%\) of these bulbs have a lifetime of less than 818 hours.
  3. Find the standard deviation of the lifetimes of bulbs from company \(Y\). Both companies sell the bulbs for the same price.
  4. State which company you would recommend. Give reasons for your answer.
    \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{}
    \end{table}
Edexcel S1 2003 June Q1
5 marks Easy -1.8
  1. In a particular week, a dentist treats 100 patients. The length of time, to the nearest minute, for each patient's treatment is summarised in the table below.
Time
(minutes)
\(4 - 7\)8\(9 - 10\)11\(12 - 16\)\(17 - 20\)
Number
of
patients
122018221513
Draw a histogram to illustrate these data.
Edexcel S1 2003 June Q2
6 marks Moderate -0.5
2. The lifetimes of batteries used for a computer game have a mean of 12 hours and a standard deviation of 3 hours. Battery lifetimes may be assumed to be normally distributed. Find the lifetime, \(t\) hours, of a battery such that 1 battery in 5 will have a lifetime longer than \(t\).
Edexcel S1 2003 June Q3
10 marks Moderate -0.8
3. A company owns two petrol stations \(P\) and \(Q\) along a main road. Total daily sales in the same week for \(P ( \pounds p )\) and for \(Q ( \pounds q )\) are summarised in the table below.
\(p\)\(q\)
Monday47605380
Tuesday53954460
Wednesday58404640
Thursday46505450
Friday53654340
Saturday49905550
Sunday43655840
When these data are coded using \(x = \frac { p - 4365 } { 100 }\) and \(y = \frac { q - 4340 } { 100 }\), $$\Sigma x = 48.1 , \Sigma y = 52.8 , \Sigma x ^ { 2 } = 486.44 , \Sigma y ^ { 2 } = 613.22 \text { and } \Sigma x y = 204.95 .$$
  1. Calculate \(S _ { x y } , S _ { x x }\) and \(S _ { y y }\).
  2. Calculate, to 3 significant figures, the value of the product moment correlation coefficient between \(x\) and \(y\).
    1. Write down the value of the product moment correlation coefficient between \(p\) and \(q\).
    2. Give an interpretation of this value.
Edexcel S1 2003 June Q4
11 marks Moderate -0.3
4. The discrete random variable \(X\) has probability function $$\mathrm { P } ( X = x ) = \begin{array} { l l } k \left( x ^ { 2 } - 9 \right) , & x = 4,5,6 \\ 0 , & \text { otherwise } \end{array}$$ where \(k\) is a positive constant.
  1. Show that \(k = \frac { 1 } { 50 }\).
  2. Find \(\mathrm { E } ( X )\) and \(\operatorname { Var } ( X )\).
  3. Find \(\operatorname { Var } ( 2 X - 3 )\).
Edexcel S1 2003 June Q5
12 marks Easy -1.2
5. The random variable \(X\) represents the number on the uppermost face when a fair die is thrown.
  1. Write down the name of the probability distribution of \(X\).
  2. Calculate the mean and the variance of \(X\). Three fair dice are thrown and the numbers on the uppermost faces are recorded.
  3. Find the probability that all three numbers are 6 .
  4. Write down all the different ways of scoring a total of 16 when the three numbers are added together.
  5. Find the probability of scoring a total of 16 .
Edexcel S1 2003 June Q6
16 marks Moderate -0.8
6. The number of bags of potato crisps sold per day in a bar was recorded over a two-week period. The results are shown below. $$20,15,10,30,33,40,5,11,13,20,25,42,31,17$$
  1. Calculate the mean of these data.
  2. Draw a stem and leaf diagram to represent these data.
  3. Find the median and the quartiles of these data. An outlier is an observation that falls either \(1.5 \times\) (interquartile range) above the upper quartile or \(1.5 \times\) (interquartile range) below the lower quartile.
  4. Determine whether or not any items of data are outliers.
  5. On graph paper draw a box plot to represent these data. Show your scale clearly.
  6. Comment on the skewness of the distribution of bags of crisps sold per day. Justify your answer.
Edexcel S1 2003 June Q7
16 marks Moderate -0.8
  1. Eight students took tests in mathematics and physics. The marks for each student are given in the table below where \(m\) represents the mathematics mark and \(p\) the physics mark.
\multirow{2}{*}{}Student
\(A\)B\(C\)D\(E\)\(F\)G\(H\)
\multirow{2}{*}{Mark}\(m\)9141310782017
\(p\)1123211519103126
A science teacher believes that students' marks in physics depend upon their mathematical ability. The teacher decides to investigate this relationship using the test marks.
  1. Write down which is the explanatory variable in this investigation.
  2. Draw a scatter diagram to illustrate these data.
  3. Showing your working, find the equation of the regression line of \(p\) on \(m\).
  4. Draw the regression line on your scatter diagram. A ninth student was absent for the physics test, but she sat the mathematics test and scored 15 .
  5. Using this model, estimate the mark she would have scored in the physics test.
AQA S1 2005 January Q1
7 marks Moderate -0.3
1 Each Monday, Azher has a stall at a town's outdoor market. The table below shows, for each of a random sample of 10 Mondays during 2003, the air temperature, \(x ^ { \circ } \mathrm { C }\), at 9 am and Azher's takings, £y.
Monday\(\mathbf { 1 }\)\(\mathbf { 2 }\)\(\mathbf { 3 }\)\(\mathbf { 4 }\)\(\mathbf { 5 }\)\(\mathbf { 6 }\)\(\mathbf { 7 }\)\(\mathbf { 8 }\)\(\mathbf { 9 }\)\(\mathbf { 1 0 }\)
\(\boldsymbol { x }\)2691813712134
\(\boldsymbol { y }\)9710313624512178145128141312
  1. A scatter diagram of these data is shown below. \includegraphics[max width=\textwidth, alt={}, center]{7faa4a2d-f5cc-4cc3-a3a9-5d8290ceabdc-2_901_1068_1078_447} Give two distinct comments, in context, on what this diagram reveals.
  2. One of the Mondays is found to be Easter Monday, the busiest Monday market of the year. Identify which Monday this is most likely to be.
  3. Removing the data for the Monday you identified in part (b), calculate the value of the product moment correlation coefficient for the remaining 9 pairs of values of \(x\) and \(y\).
  4. Name one other variable that would have been likely to affect Azher's takings at this town's outdoor market.
    (l mark)
AQA S1 2005 January Q2
9 marks Moderate -0.3
2 The volume, in millilitres, of lemonade in mini-cans may be assumed to be normally distributed with a standard deviation of 3.5. The volumes, in millilitres, of lemonade in a random sample of 12 mini-cans were as follows.
155148156149147156
157156150154148154
  1. Construct a \(98 \%\) confidence interval for the mean volume of lemonade in a mini-can, giving the limits to one decimal place.
  2. On each mini-can is printed " 150 ml ". Comment on this, using the given sample and your confidence interval in part (a).
  3. State why, in part (a), use of the Central Limit Theorem was not necessary.
AQA S1 2005 January Q3
12 marks Moderate -0.8
3 [Figure 1, printed on the insert, is provided for use in this question.]
A parcel delivery company has a depot on the outskirts of a town. Each weekday, a van leaves the depot to deliver parcels across a nearby area. The table below shows, for a random sample of 10 weekdays, the number, \(x\), of parcels to be delivered and the total time, \(y\) minutes, that the van is out of the depot.
\(\boldsymbol { x }\)9162211192614101117
\(\boldsymbol { y }\)791271721091522141318094148
  1. On Figure 1, plot a scatter diagram of these data.
  2. Calculate the equation of the least squares regression line of \(y\) on \(x\) and draw your line on Figure 1.
  3. Use your regression equation to estimate the total time that the van is out of the depot when delivering:
    1. 15 parcels;
    2. 35 parcels. Comment on the likely reliability of each of your estimates.
  4. The time that the van is out of the depot delivering parcels may be thought of as the time needed to travel to and from the area plus an amount of time proportional to the number of parcels to be delivered. Given that the regression line of \(y\) on \(x\) is of the form \(y = a + b x\), give an interpretation, in context, for each of your values of \(a\) and \(b\).
    (2 marks)