Questions — Edexcel S1 (606 questions)

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Edexcel S1 2022 January Q7
11 marks Standard +0.3
7. A bag contains \(n\) marbles of which 7 are green. From the bag, 3 marbles are selected at random.
The random variable \(X\) represents the number of green marbles selected.
The cumulative distribution function of \(X\) is given by
\(x\)0123
\(\mathrm {~F} ( x )\)\(a\)\(b\)\(\frac { 37 } { 38 }\)1
  1. Show that \(n ( n - 1 ) ( n - 2 ) = 7980\)
  2. Verify that \(n = 21\) satisfies the equation in part (a). Given that \(n = 21\)
  3. find the exact value of \(a\) and the exact value of \(b\)
    \includegraphics[max width=\textwidth, alt={}]{fa1cb8a2-dab9-4133-b7a1-9108888c37d7-28_2655_1947_114_116}
Edexcel S1 2017 June Q1
8 marks Easy -1.2
  1. Nina weighed a random sample of 50 carrots from her shop and recorded the weight, in grams to the nearest gram, for each carrot. The results are summarised below.
Weight of carrotFrequency (f)Weight midpoint \(( \boldsymbol { x }\) grams \()\)
\(45 - 54\)549.5
\(55 - 59\)1057
\(60 - 64\)2262
\(65 - 74\)1369.5
$$\text { (You may use } \sum \mathrm { f } x ^ { 2 } = 192102.5 \text { ) }$$
  1. Use linear interpolation to estimate the median weight of these carrots.
  2. Find an estimate for the mean weight of these carrots.
  3. Find an estimate for the standard deviation of the weights of these carrots. A carrot is selected at random from Nina's shop.
  4. Estimate the probability that the weight of this carrot is more than 70 grams.
Edexcel S1 2017 June Q2
11 marks Easy -1.2
2. The box plot shows the times, \(t\) minutes, it takes a group of office workers to travel to work. \includegraphics[max width=\textwidth, alt={}, center]{7d45bacd-20ac-49b4-8f3f-613edf3739f9-04_365_1237_351_356}
  1. Find the range of the times.
  2. Find the interquartile range of the times.
  3. Using the quartiles, describe the skewness of these data. Give a reason for your answer. Chetna believes that house prices will be higher if the time to travel to work is shorter. She asks a random sample of these office workers for their house prices \(\pounds x\), where \(x\) is measured in thousands, and obtains the following statistics $$\mathrm { S } _ { x x } = 5514 \quad \mathrm {~S} _ { x t } = 10 \quad \mathrm {~S} _ { t t } = 1145.6$$
  4. Calculate the product moment correlation coefficient between \(x\) and \(t\).
  5. State, giving a reason, whether or not your correlation coefficient supports Chetna's belief. Adam and Betty are part of the group of office workers and they have both moved house. Adam's time to travel to work changes from 32 minutes to 36 minutes. Betty's time to travel to work changes from 38 minutes to 58 minutes. Outliers are defined as values that are more than 1.5 times the interquartile range above the upper quartile.
  6. Showing all necessary calculations, determine how the box plot of times to travel to work will change and draw a new box plot on the grid on page 5. \includegraphics[max width=\textwidth, alt={}, center]{7d45bacd-20ac-49b4-8f3f-613edf3739f9-05_499_1413_2122_180}
Edexcel S1 2017 June Q3
12 marks Standard +0.3
  1. At a school athletics day, the distances, in metres, achieved by students in the long jump are modelled by the normal distribution with mean 3.3 m and standard deviation 0.6 m
    1. Find an estimate for the proportion of students who jump less than 2.5 m
    The long jump competition consists of 2 jumps. All the students can take part in the first jump and the \(40 \%\) who jump the greatest distance in their first jump qualify for the second jump.
  2. Find an estimate for the minimum distance achieved in the first jump in order to qualify for the second jump.
    Give your answer correct to 4 significant figures.
  3. Find an estimate for the median distance achieved in the first jump by those who qualify for the second jump. The distance of the second jump is independent of the distance of the first jump and is modelled with the same normal distribution. Students who jump a distance greater than 4.1 m in their second jump receive a certificate. At the start of the long jump competition, a student is selected at random.
  4. Find the probability that this student will receive a certificate.
Edexcel S1 2017 June Q4
12 marks Moderate -0.3
4.The partially completed tree diagram,where \(p\) and \(q\) are probabilities,gives information about Andrew's journey to work each day. \includegraphics[max width=\textwidth, alt={}, center]{7d45bacd-20ac-49b4-8f3f-613edf3739f9-12_661_794_395_511} \(R\) represents the event that it is raining
W represents the event that Andrew walks to work \(B\) represents the event that Andrew takes the bus to work \(C\) represents the event that Andrew cycles to work Given that \(\mathrm { P } ( B ) = 0.26\)
  1. find the value of \(p\) Given also that \(\mathrm { P } \left( R ^ { \prime } \mid W \right) = 0.175\)
  2. find the value of \(q\)
  3. Find the probability that Andrew cycles to work. Given that Andrew did not cycle to work on Friday,
  4. find the probability that it was raining on Friday.
Edexcel S1 2017 June Q5
15 marks Moderate -0.3
  1. Tomas is studying the relationship between temperature and hours of sunshine in Seapron. He records the midday temperature, \(t ^ { \circ } \mathrm { C }\), and the hours of sunshine, \(s\) hours, for a random sample of 9 days in October. He calculated the following statistics
$$\sum s = 15 \quad \sum s ^ { 2 } = 44.22 \quad \sum t = 127 \quad \mathrm {~S} _ { t t } = 10.89$$
  1. Calculate \(\mathrm { S } _ { s s }\) Tomas calculated the product moment correlation coefficient between \(s\) and \(t\) to be 0.832 correct to 3 decimal places.
  2. State, giving a reason, whether or not this correlation coefficient supports the use of a linear regression model to describe the relationship between midday temperature and hours of sunshine.
  3. State, giving a reason, why the hours of sunshine would be the explanatory variable in a linear regression model between midday temperature and hours of sunshine.
  4. Find \(\mathrm { S } _ { s t }\)
  5. Calculate a suitable linear regression equation to model the relationship between midday temperature and hours of sunshine.
  6. Calculate the standard deviation of \(s\) Tomas uses this model to estimate the midday temperature in Seapron for a day in October with 5 hours of sunshine.
  7. State the value of Tomas' estimate. Given that the values of \(s\) are all within 2 standard deviations of the mean,
  8. comment, giving your reason, on the reliability of this estimate.
Edexcel S1 2017 June Q6
17 marks Moderate -0.3
  1. A biased coin has probability 0.4 of showing a head. In an experiment, the coin is spun until a head appears. If a head has not appeared after 4 spins, the coin is not spun again. The random variable \(X\) represents the number of times the coin is spun.
For example, \(X = 3\) if the first two spins do not show a head but the third spin does show a head. The coin would not then be spun a fourth time since the coin has already shown a head.
  1. Show that \(\mathrm { P } ( X = 3 ) = 0.144\) The table gives some values for the probability distribution of \(X\)
    \(x\)1234
    \(\mathrm { P } ( X = x )\)0.240.144
    1. Write down the value of \(\mathrm { P } ( X = 1 )\)
    2. Find \(\mathrm { P } ( X = 4 )\)
  3. Find \(\mathrm { E } ( X )\)
  4. Find \(\operatorname { Var } ( X )\) The random variable \(H\) represents the number of heads obtained when the coin is spun in the experiment.
  5. Explain why \(H\) can only take the values 0 and 1 and find the probability distribution of \(H\).
  6. Write down the value of
    1. \(\mathrm { P } ( \{ X = 3 \} \cap \{ H = 0 \} )\)
    2. \(\mathrm { P } ( \{ X = 4 \} \cap \{ H = 0 \} )\) The random variable \(S = X + H\)
  7. Find the probability distribution of \(S\)
Edexcel S1 2017 October Q1
14 marks Easy -1.2
  1. At the start of a course, an instructor asked a group of 80 apprentices to estimate the length of a piece of pipe. The error (true length - estimated length) was recorded in centimetres. The results are summarised in the box plot below. \includegraphics[max width=\textwidth, alt={}, center]{77ae01cd-2b58-48ab-889f-272e27ecf99d-02_291_1445_397_246}
    1. Find the range for these data.
    2. Find the interquartile range for these data.
    One month later, the instructor asked the 80 apprentices to estimate the length of a different piece of pipe and recorded their errors. The results are summarised in the table below.
    Error ( \(\boldsymbol { e }\) cm)Number of apprentices
    \(- 40 < e \leqslant - 16\)2
    \(- 16 < e \leqslant - 8\)18
    \(- 8 < e \leqslant 0\)33
    \(0 < e \leqslant 8\)14
    \(8 < e \leqslant 16\)10
    \(16 < e \leqslant 40\)3
  2. Use linear interpolation to estimate the median error for these data.
  3. Show that the upper quartile for these data, to the nearest centimetre, is 4 . For these data, the lower quartile is - 8 and the five worst errors were \(- 25 , - 21,18,23,28\) An outlier is a value that falls either more than \(1.5 \times\) (interquartile range) above the upper quartile or more than \(1.5 \times\) (interquartile range) below the lower quartile.
    1. Show that there are only 2 outliers for these data.
    2. Draw a box plot for these data on the grid on page 3.
  5. State, giving reasons, whether or not the apprentices' ability to estimate the length of a piece of pipe has improved over the first month of the course. \includegraphics[max width=\textwidth, alt={}, center]{77ae01cd-2b58-48ab-889f-272e27ecf99d-03_412_1520_2222_173}
Edexcel S1 2017 October Q2
11 marks Moderate -0.8
  1. The Venn diagram, where \(w , x , y\) and \(z\) are probabilities, shows the probabilities of a group of students buying each of 3 magazines.
A represents the event that a student buys magazine \(A\) and \(\mathrm { P } ( A ) = 0.60\) \(B\) represents the event that a student buys magazine \(B\) and \(\mathrm { P } ( B ) = 0.15\) \(C\) represents the event that a student buys magazine \(C\) and \(\mathrm { P } ( C ) = 0.35\) \includegraphics[max width=\textwidth, alt={}, center]{77ae01cd-2b58-48ab-889f-272e27ecf99d-06_504_755_641_596}
  1. State which two of the three events \(A\), \(B\) and \(C\) are mutually exclusive. The events \(A\) and \(C\) are independent.
  2. Show that \(w = 0.21\)
  3. Find the value of \(x\), the value of \(y\) and the value of \(z\).
  4. Find the probability that a student selected at random buys only one of these magazines.
  5. Find the probability that a student selected at random buys magazine \(B\) or magazine \(C\).
  6. Find \(\mathrm { P } ( A \mid [ B \cup C ] )\)
Edexcel S1 2017 October Q3
12 marks Standard +0.3
3. Hei and Tang are designing some pieces of art. They collected a large number of sticks. The random variable \(L\) represents the length of a stick in centimetres and has a normal distribution with mean \(\mu\) and standard deviation \(\sigma\). They sorted the sticks into lengths and painted them.
They found that \(60 \%\) of the sticks were longer than 45 cm and these were painted red, whilst \(15 \%\) of the sticks were shorter than 35 cm and these were painted blue. The remaining sticks were painted yellow.
  1. Show that \(\mu\) and \(\sigma\) satisfy $$45 + 0.2533 \sigma = \mu$$
  2. Find a second equation in \(\mu\) and \(\sigma\).
  3. Hence find the value of \(\mu\) and the value of \(\sigma\).
  4. Find
    1. \(\mathrm { P } ( L > 35 \mid L < 45 )\)
    2. \(\mathrm { P } ( L < 45 \mid L > 35 )\) Hei created her piece of art using a random selection of blue and yellow sticks.
      Tang created his piece of art using a random selection of red and yellow sticks.
      Hei and Tang each used the same number of sticks to create their piece of art.
      George is viewing Hei's and Tang's pieces of art. He finds a yellow stick on the floor that has fallen from one of these pieces.
  5. With reference to your answers to part (d), state, giving a reason, whether the stick is more likely to have fallen from Hei's or Tang's piece of art.
Edexcel S1 2017 October Q4
8 marks Moderate -0.8
  1. The following incomplete tree diagram shows the relationships between the event \(A\) and the event \(B\). \includegraphics[max width=\textwidth, alt={}, center]{77ae01cd-2b58-48ab-889f-272e27ecf99d-14_799_839_351_548}
Given that \(\mathrm { P } ( B ) = \frac { 9 } { 20 }\)
  1. find \(\mathrm { P } ( A )\) and complete the tree diagram,
  2. find \(\mathrm { P } \left( A ^ { \prime } \mid B ^ { \prime } \right)\).
Edexcel S1 2017 October Q5
13 marks Moderate -0.8
  1. A company wants to pay its employees according to their performance at work. Last year's performance score \(x\) and annual salary \(y\), in thousands of dollars, were recorded for a random sample of 10 employees of the company.
The performance scores were $$\begin{array} { l l l l l l l l l l } 15 & 24 & 32 & 39 & 41 & 18 & 16 & 22 & 34 & 42 \end{array}$$ (You may use \(\sum x ^ { 2 } = 9011\) )
  1. Find the mean and the variance of these performance scores. The corresponding \(y\) values for these 10 employees are summarised by $$\sum y = 306.1 \quad \text { and } \quad \mathrm { S } _ { y y } = 546.3$$
  2. Find the mean and the variance of these \(y\) values. The regression line of \(y\) on \(x\) based on this sample is $$y = 12.0 + 0.659 x$$
  3. Find the product moment correlation coefficient for these data.
  4. State, giving a reason, whether or not the value of the product moment correlation coefficient supports the use of a regression line to model the relationship between performance score and annual salary. The company decides to use this regression model to determine future salaries.
  5. Find the proposed annual salary, in dollars, for an employee who has a performance score of 35
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}