Questions — Edexcel S1 (606 questions)

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Edexcel S1 2016 October Q2
15 marks Moderate -0.3
  1. The discrete random variable \(X\) has probability distribution
\(x\)- 2- 1123
\(\mathrm { P } ( X = x )\)\(b\)\(a\)\(a\)\(b\)\(\frac { 1 } { 5 }\)
where \(a\) and \(b\) are constants.
  1. Write down an equation for \(a\) and \(b\).
  2. Calculate \(\mathrm { E } ( X )\). Given that \(\mathrm { E } \left( X ^ { 2 } \right) = 3.5\)
    1. find a second equation in \(a\) and \(b\),
    2. hence find the value of \(a\) and the value of \(b\).
  4. Find \(\operatorname { Var } ( X )\). The random variable \(Y = 5 - 3 X\)
  5. Find \(\mathrm { P } ( Y > 0 )\).
  6. Find
    1. \(\mathrm { E } ( Y )\),
    2. \(\operatorname { Var } ( Y )\).
Edexcel S1 2016 October Q3
12 marks Standard +0.3
  1. Hugo recorded the purchases of 80 customers in the ladies fashion department of a large store. His results were as follows
20 customers bought a coat
12 customers bought a coat and a scarf
23 customers bought a pair of gloves
13 customers bought a pair of gloves and a scarf no customer bought a coat and a pair of gloves 14 customers did not buy a coat nor a scarf nor a pair of gloves.
  1. Draw a Venn diagram to represent all of this information.
  2. One of the 80 customers is selected at random.
    1. Find the probability that the customer bought a scarf.
    2. Given that the customer bought a coat, find the probability that the customer also bought a scarf.
    3. State, giving a reason, whether or not the event 'the customer bought a coat' and the event 'the customer bought a scarf' are statistically independent. Hugo had asked the member of staff selling coats and the member of staff selling gloves to encourage customers also to buy a scarf.
  3. By considering suitable conditional probabilities, determine whether the member of staff selling coats or the member of staff selling gloves has the better performance at selling scarves to their customers. Give a reason for your answer.
Edexcel S1 2016 October Q4
15 marks Moderate -0.3
  1. A doctor is studying the scans of 30 -week old foetuses. She takes a random sample of 8 scans and measures the length, \(f \mathrm {~mm}\), of the leg bone called the femur. She obtains the following results.
$$\begin{array} { l l l l l l l l } 52 & 53 & 56 & 57 & 57 & 59 & 60 & 62 \end{array}$$
  1. Show that \(\mathrm { S } _ { f f } = 80\) The doctor also measures the head circumference, \(h \mathrm {~mm}\), of each foetus and her results are summarised as $$\sum h = 2209 \quad \sum h ^ { 2 } = 610463 \quad \mathrm {~S} _ { f h } = 182$$
  2. Find \(\mathrm { S } _ { h h }\)
  3. Calculate the product moment correlation coefficient between the length of the femur and the head circumference for these data. The doctor believes that there is a linear relationship between the length of the femur and the head circumference of 30-week old foetuses.
  4. State, giving a reason, whether or not your calculation in part (c) supports the doctor's belief.
  5. Find an equation of the regression line of \(h\) on \(f\). The doctor plans in future to measure the femur length, \(f\), and then use the regression line to estimate the corresponding head circumference, \(h\). A statistician points out that there will always be the chance of an error between the true head circumference and the estimated value of the head circumference. Given that the error, \(E \mathrm {~mm}\), has the normal distribution \(\mathrm { N } \left( 0,4 ^ { 2 } \right)\)
  6. find the probability that the estimate is within 3 mm of the true value.
Edexcel S1 2016 October Q5
11 marks Challenging +1.2
  1. The label on a jar of Amy's jam states that the jar contains about 400 grams of jam. For each jar that contains less than 388 grams of jam, Amy will be fined \(\pounds 100\). If a jar contains more than 410 grams of jam then Amy makes a loss of \(\pounds 0.30\) on that jar.
The weight of jam, \(A\) grams, in a jar of Amy's jam has a normal distribution with mean \(\mu\) grams and standard deviation \(\sigma\) grams. Amy chooses \(\mu\) and \(\sigma\) so that \(\mathrm { P } ( A < 388 ) = 0.001\) and \(\mathrm { P } ( A > 410 ) = 0.0197\)
  1. Find the value of \(\mu\) and the value of \(\sigma\). Amy can sell jars of jam containing between 388 grams and 410 grams for a profit of \(\pounds 0.25\)
  2. Calculate the expected amount, in £s, that Amy receives for each jar of jam.
Edexcel S1 2016 October Q6
17 marks Easy -1.2
  1. The stem and leaf diagram gives the blood pressure, \(x \mathrm { mmHg }\), for a random sample of 19 female patients.
1012
1127788
12022344557
13129
Key: 10 | 1 means blood pressure of 101 mmHg
  1. Find the median and the quartiles for these data.
  2. Find the interquartile range ( \(Q _ { 3 } - Q _ { 1 }\) ) An outlier is a value that is greater than \(Q _ { 3 } + 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\) or less than \(Q _ { 1 } - 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\)
  3. Showing your working clearly, identify any outliers for these data.
  4. On the grid on page 21 draw a box and whisker plot to represent these data. Show any outliers clearly. The above data can be summarised by $$\sum x = 2299 \text { and } \sum x ^ { 2 } = 279709$$
  5. Calculate the mean and the standard deviation for these data. For a random sample taken from a normal distribution, a rule for determining outliers is: an outlier is more than \(2.7 \times\) standard deviation above or below the mean.
  6. Find the limits to determine outliers using this rule.
  7. State, giving a reason based on some of the above calculations, whether or not a normal distribution is a suitable model for these data. \includegraphics[max width=\textwidth, alt={}, center]{8ff7539e-fa44-4388-af8c-80656f081528-21_2281_73_308_15}
    Turn over for a spare diagram if you need to redraw your plot.
    \includegraphics[max width=\textwidth, alt={}]{8ff7539e-fa44-4388-af8c-80656f081528-24_2639_1830_121_121}
Edexcel S1 2018 October Q1
11 marks Moderate -0.8
  1. The heights above sea level ( \(h\) hundred metres) and the temperatures ( \(t ^ { \circ } \mathrm { C }\) ) at 12 randomly selected places in France, at 7 am on July 31st, were recorded.
    The data are summarised as follows
    1. Find the value of \(S _ { t t }\)
    2. Calculate the product moment correlation coefficient for these data.
    3. Interpret the relationship between \(t\) and \(h\).
    4. Find an equation of the regression line of \(t\) on \(h\).
    At 7 am on July 31st Yinka is on holiday in South Africa. He uses the regression equation to estimate the temperature when the height above sea level is 500 m .
  2. Find the estimated temperature Yinka calculates.
  3. Comment on the validity of your answer in part (e). $$\sum h = 112 \quad \sum t = 136 \quad \sum t ^ { 2 } = 1828 \quad S _ { h t } = - 236 \quad S _ { h h } = 297$$
  4. Find the value of \(S\) (2)
Edexcel S1 2018 October Q2
11 marks Easy -1.3
  1. The weights, to the nearest kilogram, of a sample of 33 female spotted hyenas living in the Serengeti are summarised in the stem and leaf diagram below.
\begin{table}[h]
\captionsetup{labelformat=empty} \caption{Weight (kg)}
3237
413345569
5122344555788999
6233
7147
84
\end{table} Totals
  1. Find the median and quartiles for the weights of the female spotted hyenas. An outlier is defined as any value greater than \(c\) or any value less than \(d\) where $$\begin{aligned} & c = Q _ { 3 } + 1.5 \left( Q _ { 3 } - Q _ { 1 } \right) \\ & d = Q _ { 1 } - 1.5 \left( Q _ { 3 } - Q _ { 1 } \right) \end{aligned}$$
  2. Showing your working clearly, identify any outliers for these data.
    (3) The weights, to the nearest kilogram, of a sample of male spotted hyenas living in the Serengeti are summarised below. \includegraphics[max width=\textwidth, alt={}, center]{0377c6e9-ab4f-477d-9236-0732fe81f25e-06_755_1568_1537_185}
  3. In the space provided in the grid above, draw a box and whisker plot to represent the weights of female spotted hyenas living in the Serengeti. Indicate clearly any outliers. (A copy of this grid is on page 9 if you need to redraw your box and whisker plot.)
  4. Compare the weights of male and female spotted hyenas living in the Serengeti. Key: 3|2 means 32
    \includegraphics[max width=\textwidth, alt={}, center]{0377c6e9-ab4f-477d-9236-0732fe81f25e-09_2658_101_107_9}
Edexcel S1 2018 October Q3
13 marks Moderate -0.8
3. The parking times, \(t\) hours, for cars in a car park are summarised below.
Time (t hours)Frequency (f)Time midpoint (m)
\(0 \leqslant t < 1\)100.5
\(1 \leqslant t < 2\)181.5
\(2 \leqslant t < 4\)153
\(4 \leqslant t < 6\)125
\(6 \leqslant t < 12\)59
$$\text { (You may use } \sum \mathrm { fm } = 182 \text { and } \sum \mathrm { fm } ^ { 2 } = 883 \text { ) }$$ A histogram is drawn to represent these data.
The bar representing the time \(1 \leqslant t < 2\) has a width of 1.5 cm and a height of 6 cm .
  1. Calculate the width and the height of the bar representing the time \(4 \leqslant t < 6\)
  2. Use linear interpolation to estimate the median parking time for the cars in the car park.
  3. Estimate the mean and the standard deviation of the parking time for the cars in the car park.
  4. Describe, giving a reason, the skewness of the data. One of these cars is selected at random.
  5. Estimate the probability that this car is parked for more than 75 minutes.
Edexcel S1 2018 October Q4
10 marks Moderate -0.3
4. Pieces of wood cladding are produced by a timber merchant. There are three types of fault, \(A , B\) and \(C\), that can appear in each piece of wood cladding. The Venn diagram shows the probabilities of a piece of wood cladding having the various types of fault. \includegraphics[max width=\textwidth, alt={}, center]{0377c6e9-ab4f-477d-9236-0732fe81f25e-14_602_1120_497_413} A piece of wood cladding is chosen at random.
  1. Find the probability that the piece of wood cladding has more than one type of fault. Fault types \(A\) and \(C\) occur independently.
  2. Find the probability that the piece of wood cladding has no faults. Given that the piece of wood cladding has fault \(A\),
  3. find the probability that it also has fault \(B\) but not fault \(C\). Two pieces of the wood cladding are selected at random.
  4. Find the probability that both have exactly 2 types of fault.
Edexcel S1 2018 October Q5
14 marks Moderate -0.3
  1. The discrete random variable \(X\) is defined by the cumulative distribution function
\(x\)12345
\(\mathrm {~F} ( x )\)\(\frac { 3 k } { 2 }\)\(4 k\)\(\frac { 15 k } { 2 }\)\(12 k\)\(\frac { 35 k } { 2 }\)
where \(k\) is a constant.
  1. Find the probability distribution of \(X\).
  2. Find \(\mathrm { P } ( 1.5 < X \leqslant 3.5 )\) The random variable \(Y = 12 - 7 X\)
  3. Calculate Var(Y)
  4. Calculate \(\mathrm { P } ( 4 X \leqslant | Y | )\)
Edexcel S1 2018 October Q6
16 marks Standard +0.3
  1. A machine makes bolts such that the length, \(L \mathrm {~cm}\), of a bolt has distribution \(L \sim \mathrm {~N} \left( 4.1,0.125 ^ { 2 } \right)\)
A bolt is selected at random.
  1. Find the probability that the length of this bolt is more than 4.3 cm .
  2. Show that \(\mathrm { P } ( 3.9 < L < 4.3 )\) is 0.890 correct to 3 decimal places. The machine makes 500 bolts.
    The cost to make each bolt is 5 pence.
    Only bolts with length between 3.9 cm and 4.3 cm can be used. These are sold for 9 pence each. All the bolts that cannot be used are recycled with a scrap value of 1 pence each.
  3. Calculate an estimate for the profit made on these 500 bolts. Following adjustments to the machine, the length of a bolt, \(B \mathrm {~cm}\), made by the machine is such that \(B \sim \mathrm {~N} \left( \mu , \sigma ^ { 2 } \right)\) Given that \(\mathrm { P } ( B > 4.198 ) = 0.025\) and \(\mathrm { P } ( B < 4.065 ) = 0.242\)
  4. find the value of \(\mu\) and the value of \(\sigma\)
  5. State, giving a reason, whether the adjustments to the machine will result in a decrease or an increase in the profit made on 500 bolts.
Edexcel S1 2022 October Q1
11 marks Moderate -0.8
  1. The stem lengths of a sample of 120 tulips are recorded in the grouped frequency table below.
Stem length (cm)Frequency
\(40 \leqslant x < 42\)12
\(42 \leqslant x < 45\)18
\(45 \leqslant x < 50\)23
\(50 \leqslant x < 55\)35
\(55 \leqslant x < 58\)24
\(58 \leqslant x < 60\)8
A histogram is drawn to represent these data.
The area of the bar representing the \(40 \leqslant x < 42\) class is \(16.5 \mathrm {~cm} ^ { 2 }\)
  1. Calculate the exact area of the bar representing the \(42 \leqslant x < 45\) class. The height of the tallest bar in the histogram is 10 cm .
  2. Find the exact height of the second tallest bar. \(Q _ { 1 }\) for these data is 45 cm .
  3. Use linear interpolation to find an estimate for
    1. \(Q _ { 2 }\)
    2. the interquartile range. One measure of skewness is given by $$\frac { Q _ { 3 } - 2 Q _ { 2 } + Q _ { 1 } } { Q _ { 3 } - Q _ { 1 } }$$
  4. By calculating this measure, describe the skewness of these data.
Edexcel S1 2022 October Q2
13 marks Moderate -0.5
  1. The production cost, \(\pounds c\) million, of a film and the total ticket sales, \(\pounds t\) million, earned by the film are recorded for a sample of 40 films.
Some summary statistics are given below. $$\sum c = 1634 \quad \sum t = 1361 \quad \sum t ^ { 2 } = 82873 \quad \sum c t = 83634 \quad \mathrm {~S} _ { c c } = 28732.1$$
  1. Find the exact value of \(\mathrm { S } _ { t t }\) and the exact value of \(\mathrm { S } _ { c t }\)
  2. Calculate the value of the product moment correlation coefficient for these data.
  3. Give an interpretation of your answer to part (b)
  4. Show that the equation of the linear regression line of \(t\) on \(c\) can be written as $$t = - 5.84 + 0.976 c$$ where the values of the intercept and gradient are given to 3 significant figures.
  5. Find the expected total ticket sales for a film with a production cost of \(\pounds 90\) million. Using the regression line in part (d)
  6. find the range of values of the production cost of a film for which the total ticket sales are less than \(80 \%\) of its production cost.
Edexcel S1 2022 October Q3
10 marks Moderate -0.5
  1. Morgan is investigating the body length, \(b\) centimetres, of squirrels.
A random sample of 8 squirrels is taken and the data for each squirrel is coded using $$x = \frac { b - 21 } { 2 }$$ The results for the coded data are summarised below $$\sum x = - 1.2 \quad \sum x ^ { 2 } = 5.1$$
  1. Find the mean of \(b\)
  2. Find the standard deviation of \(b\) A 9th squirrel is added to the sample. Given that for all 9 squirrels \(\sum x = 0\)
  3. find
    1. the body length of the 9th squirrel,
    2. the standard deviation of \(x\) for all 9 squirrels.
Edexcel S1 2022 October Q4
4 marks Moderate -0.8
  1. The cumulative distribution function of the discrete random variable \(W\), which takes only the values 6,7 and 8 , is given by
$$F ( W ) = \frac { ( w + 3 ) ( w - 1 ) } { 77 } \text { for } w = 6,7,8$$ Find \(\mathrm { E } ( W )\)
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Edexcel S1 2022 October Q5
12 marks Standard +0.3
  1. The weights, \(W\) grams, of kiwi fruit grown on a farm are normally distributed with mean 80 grams and standard deviation 8 grams.
The table shows the classifications of the kiwi fruit by their weight, where \(k\) is a positive constant.
SmallLarge
TinyPetiteExtraJumboMega
\(w < 66\)\(66 \leqslant w < 70\)\(70 \leqslant w < 80\)\(80 \leqslant w < k\)\(w \geqslant k\)
One kiwi fruit is selected at random from those grown on the farm.
  1. Find the probability that this kiwi fruit is Large. 35\% of the kiwi fruit are Jumbo.
  2. Find the value of \(k\) to one decimal place. 75\% of Tiny kiwi fruit weigh more than \(y\) grams.
  3. Find the value of \(y\) giving your answer to one decimal place.
Edexcel S1 2022 October Q6
11 marks Standard +0.3
  1. The Venn diagram shows the events \(A , B , C\) and \(D\), where \(p , q , r\) and \(s\) are probabilities. \includegraphics[max width=\textwidth, alt={}, center]{1fda59cb-059e-4850-810f-cc3e69bc058e-20_504_826_296_621}
    1. Write down the value of
      1. \(\mathrm { P } ( A )\)
      2. \(\mathrm { P } ( A \mid B )\)
      3. \(\mathrm { P } ( A \mid C )\)
    Given that \(\mathrm { P } \left( B ^ { \prime } \cap D ^ { \prime } \right) = \frac { 7 } { 10 }\) and \(\mathrm { P } ( C \mid D ) = \frac { 3 } { 5 }\)
  2. find the exact value of \(q\) and the exact value of \(r\) Given also that \(\mathrm { P } \left( B \cup C ^ { \prime } \right) = \frac { 5 } { 8 }\)
  3. find the exact value of \(s\)
Edexcel S1 2022 October Q7
14 marks Standard +0.3
  1. Adana selects one number at random from the distribution of \(X\) which has the following probability distribution.
\(x\)0510
\(\mathrm { P } ( X = x )\)0.10.20.7
  1. Given that the number selected by Adana is not 5 , write down the probability it is 0
  2. Show that \(\mathrm { E } \left( X ^ { 2 } \right) = 75\)
  3. Find \(\operatorname { Var } ( X )\)
  4. Find \(\operatorname { Var } ( 4 - 3 X )\) Bruno and Charlie each independently select one number at random from the distribution of \(X\)
  5. Find the probability that the number Bruno selects is greater than the number Charlie selects. Devika multiplies Bruno's number by Charlie's number to obtain a product, \(D\)
  6. Determine the probability distribution of \(D\)
Edexcel S1 2023 October Q1
11 marks Moderate -0.8
  1. Sally plays a game in which she can either win or lose.
A turn consists of up to 3 games. On each turn Sally plays the game up to 3 times. If she wins the first 2 games or loses the first 2 games, then she will not play the 3rd game.
  • The probability that Sally wins the first game in a turn is 0.7
  • If Sally wins a game the probability that she wins the next game is 0.6
  • If Sally loses a game the probability that she wins the next game is 0.2
    1. Use this information to complete the tree diagram on page 3
    2. Find the probability that Sally wins the first 2 games in a turn.
    3. Find the probability that Sally wins exactly 2 games in a turn.
Given that Sally wins 2 games in a turn,
  • find the probability that she won the first 2 games. Given that Sally won the first game in a turn,
  • find the probability that she won 2 games. 1st game 2nd game win
    •
    Edexcel S1 2023 October Q2
    13 marks Easy -1.2
    1. The weights, to the nearest kilogram, of a sample of 33 red kangaroos taken in December are summarised in the stem and leaf diagram below.
    Weight (kg)Totals
    16(1)
    236(2)
    3246(3)
    42556678(7)
    534777899(8)
    6022338(7)
    728(2)
    826(2)
    94(1)
    Key: 3 | 2 represents 32 kg
    1. Find
      1. the value of the median
      2. the value of \(Q _ { 1 }\) and the value of \(Q _ { 3 }\) for the weights of these red kangaroos. For these data an outlier is defined as a value that is
        greater than \(Q _ { 3 } + 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\) or smaller than \(Q _ { 1 } - 1.5 \times \left( Q _ { 3 } - Q _ { 1 } \right)\)
    2. Show that there are 2 outliers for these data. Figure 1 on page 7 shows a box plot for the weights of the same 33 red kangaroos taken in February, earlier in the year.
    3. In the space on Figure 1, draw a box plot to represent the weights of these red kangaroos in December.
    4. Compare the distribution of the weights of red kangaroos taken in February with the distribution of the weights of red kangaroos taken in December of the same year. You should interpret your comparisons in the context of the question.
      \includegraphics[max width=\textwidth, alt={}]{f94b29e0-081f-45e8-99a7-ac835eec91e5-07_2267_51_307_36}
      \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{f94b29e0-081f-45e8-99a7-ac835eec91e5-07_766_1803_1777_132} \captionsetup{labelformat=empty} \caption{Figure 1}
      \end{figure} Turn over for a spare grid if you need to redraw your box plot. \begin{figure}[h]
      \includegraphics[alt={},max width=\textwidth]{f94b29e0-081f-45e8-99a7-ac835eec91e5-09_901_1833_1653_114} \captionsetup{labelformat=empty} \caption{Figure 1}
      \end{figure} \begin{verbatim} (Total for Question 2 is 13 marks) \end{verbatim}
    Edexcel S1 2023 October Q3
    12 marks Easy -1.2
      1. Bob shops at a market each week. The event that
    Bob buys carrots is denoted by \(C\) Bob buys onions is denoted by \(O\) At each visit, Bob may buy neither, or one, or both of these items. The probability that Bob buys carrots is 0.65
    Bob does not buy onions is 0.3
    Bob buys onions but not carrots is 0.15
    The Venn diagram below represents the events \(C\) and \(O\)
    [diagram]

    where \(w , x , y\) and \(z\) are probabilities.
    1. Find the value of \(w\), the value of \(x\), the value of \(y\) and the value of \(z\) For one visit to the market,
    2. find the probability that Bob buys either carrots or onions but not both.
    3. Show that the events \(C\) and \(O\) are not independent.
      (ii) \(F , G\) and \(H\) are 3 events. \(F\) and \(H\) are mutually exclusive. \(F\) and \(G\) are independent. Given that $$\mathrm { P } ( F ) = \frac { 2 } { 7 } \quad \mathrm { P } ( H ) = \frac { 1 } { 4 } \quad \mathrm { P } ( F \cup G ) = \frac { 5 } { 8 }$$
    4. find \(\operatorname { P } ( F \cup H )\)
    5. find \(\mathrm { P } ( G )\)
    6. find \(\operatorname { P } ( F \cap G )\)
    Edexcel S1 2023 October Q4
    12 marks Moderate -0.3
    1. The discrete random variable \(X\) has the following probability distribution.
    \(x\)1234
    \(\mathrm { P } ( X = x )\)\(\frac { 1 } { 10 }\)\(\frac { 1 } { 5 }\)\(\frac { 3 } { 10 }\)\(\frac { 2 } { 5 }\)
    1. Show that \(\mathrm { E } \left( \frac { 1 } { X } \right) = \frac { 2 } { 5 }\)
    2. Find \(\operatorname { Var } \left( \frac { 1 } { X } \right)\) The random variable \(Y = \frac { 30 } { X }\)
    3. Find
      1. \(\mathrm { E } ( Y )\)
      2. \(\operatorname { Var } ( Y )\)
    4. Find \(\mathrm { P } ( X < 3 \mid Y < 20 )\)
    Edexcel S1 2023 October Q5
    15 marks Standard +0.3
    1. The weights, \(X\) grams, of a particular variety of fruit are normally distributed with
    $$X \sim \mathrm {~N} \left( 210,25 ^ { 2 } \right)$$ A fruit of this variety is selected at random.
    1. Show that the probability that the weight of this fruit is less than 240 grams is 0.8849
    2. Find the probability that the weight of this fruit is between 190 grams and 240 grams.
    3. Find the value of \(k\) such that \(\mathrm { P } ( 210 - k < X < 210 + k ) = 0.95\) A wholesaler buys large numbers of this variety of fruit and classifies the lightest \(15 \%\) as small.
    4. Find the maximum weight of a fruit that is classified as small. You must show your working clearly. The weights, \(Y\) grams, of a second variety of this fruit are normally distributed with $$Y \sim \mathrm {~N} \left( \mu , \sigma ^ { 2 } \right)$$ Given that \(5 \%\) of these fruit weigh less than 152 grams and \(40 \%\) weigh more than 180 grams,
    5. calculate the mean and standard deviation of the weights of this variety of fruit.
    Edexcel S1 2023 October Q6
    12 marks Moderate -0.3
    1. The variables \(x\) and \(y\) have the following regression equations based on the same 12 observations.
    \cline { 2 - 2 } \multicolumn{1}{c|}{}Regression equation
    \(y\) on \(x\)\(y = 1.4 x + 1.5\)
    \(x\) on \(y\)\(x = 1.2 + 0.2 y\)
      1. Find the point of intersection of these lines.
      2. Hence show that \(\sum x = 25\) Given that $$\sum x y = \frac { 6961 } { 60 }$$
    2. Find \(S _ { x y }\)
    3. Find the product moment correlation coefficient between \(x\) and \(y\)
    Edexcel S1 2018 Specimen Q1
    12 marks Moderate -0.8
    1. The percentage oil content, \(p\), and the weight, \(w\) milligrams, of each of 10 randomly selected sunflower seeds were recorded. These data are summarised below.
    $$\sum w ^ { 2 } = 41252 \quad \sum w p = 27557.8 \quad \sum w = 640 \quad \sum p = 431 \quad \mathrm {~S} _ { p p } = 2.72$$
    1. Find the value of \(\mathrm { S } _ { w w }\) and the value of \(\mathrm { S } _ { w p }\)
    2. Calculate the product moment correlation coefficient between \(p\) and \(w\)
    3. Give an interpretation of your product moment correlation coefficient. The equation of the regression line of \(p\) on \(w\) is given in the form \(p = a + b w\)
    4. Find the equation of the regression line of \(p\) on \(w\)
    5. Hence estimate the percentage oil content of a sunflower seed which weighs 60 milligrams. \(\_\_\_\_\) VAYV SIHI NI JIIIM ION OC
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