Legacy S1 — Statistics 1: Edexcel A‑Level Maths questions

Edexcel A-Level Maths past-paper questions on L.S1 Legacy S1 — Statistics 1, 2010–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.

All 104 questions on Legacy S1 — Statistics 1, as a list

June 2018, Legacy S1, Q1 (4 marks): The discrete random variable X has the following probability distribution x 2 4 7 10 P(X = x) a b 0.1 c where a, b and c are probabilities. The cumulative distr
June 2018, Legacy S1, Q2 (12 marks): The following grouped frequency distribution summarises the number of minutes, to the nearest minute, that a random sample of 100 motorists were delayed by road
June 2018, Legacy S1, Q3 (5 marks): The random variable Y has a normal distribution with mean µ and standard deviation σ The P(Y > 17) = 0.4 Find (a) P(µ < Y < 17) (1) (b) P(µ – σ < Y < 17) (4)
June 2018, Legacy S1, Q4 (13 marks): A bag contains 64 coloured beads. There are r red beads, y yellow beads and 1 green bead and r + y + 1 = 64 Two beads are selected at random, one at a time with
June 2018, Legacy S1, Q5 (14 marks): The score when a spinner is spun is given by the discrete random variable X with the following probability distribution, where a and b are probabilities. x – 1
June 2018, Legacy S1, Q6 (14 marks): A group of climbers collected information about the height above sea level, h metres, and the air temperature, t °C, at the same time at 8 different points on t
June 2018, Legacy S1, Q7 (13 marks): Farmer Adam grows potatoes. The weights of potatoes, in grams, grown by Adam are normally distributed with a mean of 140 g and a standard deviation of 40 g. Ada
June 2017, Legacy S1, Q1 (14 marks): A clothes shop manager records the weekly sales figures, £ s, and the average weekly temperature, t °C, for 6 weeks during the summer. The sales figures were co
June 2017, Legacy S1, Q2 (14 marks): An estate agent is studying the cost of office space in London. He takes a random sample of 90 offices and calculates the cost, £x per square foot. His results
June 2017, Legacy S1, Q3 (11 marks): The Venn diagram shows three events A, B and C, where p, q, r, s and t are probabilities. r A B C 0.08 s t p q P(A) = 0.5, P(B) = 0.6 and P(C) = 0.25 and the ev
June 2017, Legacy S1, Q4 (6 marks): The discrete random variable X has probability distribution x –1 0 1 2 P(X = x) a b b c The cumulative distribution function of X is given by x –1 0 1 2 F(x) 1
June 2017, Legacy S1, Q5 (12 marks): Yuto works in the quality control department of a large company. The time, T minutes, it takes Yuto to analyse a sample is normally distributed with mean 18 min
June 2017, Legacy S1, Q6 (18 marks): The score, X, for a biased spinner is given by the probability distribution x 0 3 6 P(X = x) 1 12 2 3 1 4 Find (a) E(X) (2) (b) Var(X) (3) A biased coin has one
June 2016, Legacy S1, Q1 (11 marks): A biologist is studying the behaviour of bees in a hive. Once a bee has located a source of food, it returns to the hive and performs a dance to indicate to the
June 2016, Legacy S1, Q2 (15 marks): The discrete random variable X has the following probability distribution, where p and q are constants. x –2 –1 1 2 3 2 2 P(X = x) p q 0.2 0.3 p (a) Write down
June 2016, Legacy S1, Q3 (10 marks): Before going on holiday to Seapron, Tania records the weekly rainfall (x mm) at Seapron for 8 weeks during the summer. Her results are summarised as x
June 2016, Legacy S1, Q4 (13 marks): The Venn diagram shows the probabilities of customer bookings at Harry’s hotel. R is the event that a customer books a room B is the event that a customer books
June 2016, Legacy S1, Q5 (17 marks): A midwife records the weights, in kg, of a sample of 50 babies born at a hospital. Her results are given in the table below. Weight (w kg) Frequency (f) Weight
June 2016, Legacy S1, Q6 (9 marks): The time, in minutes, taken by men to run a marathon is modelled by a normal distribution with mean 240 minutes and standard deviation 40 minutes. (a) Find the
June 2015, Legacy S1, Q1 (14 marks): Each of 60 students was asked to draw a 20° angle without using a protractor. The size of each angle drawn was measured. The results are summarised in the box p
June 2015, Legacy S1, Q2 (8 marks): An estate agent recorded the price per square metre, p £/m2, for 7 two-bedroom houses. He then coded the data using the coding q = p a b – , where a and b are p
June 2015, Legacy S1, Q3 (13 marks): A college has 80 students in Year 12. 20 students study Biology 28 students study Chemistry 30 students study Physics 7 students study both Biology and Chemistr
June 2015, Legacy S1, Q4 (14 marks): Statistical models can provide a cheap and quick way to describe a real world situation. (a) Give two other reasons why statistical models are used. (2) A scien
June 2015, Legacy S1, Q5 (14 marks): In a quiz, a team gains 10 points for every question it answers correctly and loses 5 points for every question it does not answer correctly. The probability of
June 2015, Legacy S1, Q6 (12 marks): The random variable Z ~ N(0, 1) A is the event Z 1.1 B is the event Z –1.9 C is the event –1.5 Z 1.5 (a) Find (i) P(A) (ii) P(B) (iii) P(C) (iv) P(A ∪ C) (6) Th
June 2014, Legacy S1, Q1 (9 marks): A random sample of 35 homeowners was taken from each of the villages Greenslax and Penville and their ages were recorded. The results are summarised in the back
June 2014, Legacy S1, Q2 (4 marks): The mark, x, scored by each student who sat a statistics examination is coded using y = 1.4x – 20 The coded marks have mean 60.8 and standard deviation 6.60 Fin
June 2014, Legacy S1, Q3 (13 marks): The table shows data on the number of visitors to the UK in a month, v (1000s), and the amount of money they spent, m (£ millions), for each of 8 months. Number
June 2014, Legacy S1, Q4 (9 marks): In a factory, three machines, J, K and L, are used to make biscuits. Machine J makes 25% of the biscuits. Machine K makes 45% of the biscuits. The rest of the b
June 2014, Legacy S1, Q5 (10 marks): The discrete random variable X has the probability function P 2, 4, 6 otherwise ( ) ( ) X x kx x k x x = = = − = ⎧ ⎨ ⎪⎪ ⎩ ⎪ ⎪ 2 8 0 where k is a constant. (a) S
June 2014, Legacy S1, Q6 (11 marks): The times, in seconds, spent in a queue at a supermarket by 85 randomly selected customers, are summarised in the table below. Time (seconds) Number of customer
June 2014, Legacy S1, Q7 (12 marks): The heights of adult females are normally distributed with mean 160 cm and standard deviation 8 cm. (a) Find the probability that a randomly selected adult fema
June 2014, Legacy S1, Q8 (7 marks): For the events A and B, P(Ac B) = 0.22 and P(Ac Bc) = 0.18 (a) Find P(A). (1) (b) Find P(A B). (1) Given that P(A | B) = 0.6 (c) find P(A B). (3) (d) De
June 2014, Legacy S1 (01R), Q1 (9 marks): The discrete random variable X has probability distribution x í í 1 3 5 P(X = x) 0.4 p 0.05 0.15 p (a) Show that p = 0.2 (2) Find (b) E(X) (2) (c) F(0) (1)
June 2014, Legacy S1 (01R), Q2 (5 marks): The discrete random variable X has probability distribution P(X = x) = 1 10 x = 1, 2, 3, … 10 (a) Write down the name given to this distribution. (1) (b) Write
June 2014, Legacy S1 (01R), Q3 (16 marks): A large company is analysing how much money it spends on paper in its offices every year. The number of employees, x, and the amount of money spent on paper, p
June 2014, Legacy S1 (01R), Q4 (9 marks): A and B are two events such that P(B) = 1 2 P(A | B) = 2 5 P(A B) = 13 20 (a) Find P(A B). (2) (b) Draw a Venn diagram to show the events A, B and all the a
June 2014, Legacy S1 (01R), Q5 (12 marks): The table shows the time, to the nearest minute, spent waiting for a taxi by each of 80 people one Sunday afternoon. Waiting time (in minutes) Frequency 2–4 15
June 2014, Legacy S1 (01R), Q6 (13 marks): The time taken, in minutes, by children to complete a mathematical puzzle is assumed to be normally distributed with mean μ and standard deviation ı The puzzle
June 2014, Legacy S1 (01R), Q7 (11 marks): In a large company, 78% of employees are car owners, 30% of these car owners are also bike owners, 85% of those who are not car owners are bike owners. (a) Draw
June 2013, Legacy S1, Q1 (13 marks): A meteorologist believes that there is a relationship between the height above sea level, h m, and the air temperature, t °C. Data is collected at the same time
June 2013, Legacy S1, Q2 (11 marks): The marks of a group of female students in a statistics test are summarised in Figure 1 Figure 1 (a) Write down the mark which is exceeded by 75% of the female
June 2013, Legacy S1, Q3 (12 marks): In a company the 200 employees are classified as full-time workers, part-time workers or contractors. The table below shows the number of employees in each cate
June 2013, Legacy S1, Q4 (14 marks): The following table summarises the times, t minutes to the nearest minute, recorded for a group of students to complete an exam. Time (minutes) t 11 – 20 21 – 2
June 2013, Legacy S1, Q5 (15 marks): A biased die with six faces is rolled. The discrete random variable X represents the score on the uppermost face. The probability distribution of X is shown in
June 2013, Legacy S1, Q6 (10 marks): The weight, in grams, of beans in a tin is normally distributed with mean and standard deviation 7.8 Given that 10% of tins contain less than 200 g, find (a)
June 2013, Legacy S1 (01R), Q1 (10 marks): Sammy is studying the number of units of gas, g, and the number of units of electricity, e, used in her house each week. A random sample of 10 weeks use was rec
June 2013, Legacy S1 (01R), Q2 (4 marks): The discrete random variable X takes the values 1, 2 and 3 and has cumulative distribution function F(x) given by x 1 2 3 F(x) 0.4 0.65 1 (a) Find the probabili
June 2013, Legacy S1 (01R), Q3 (13 marks): An agriculturalist is studying the yields, y kg, from tomato plants. The data from a random sample of 70 tomato plants are summarised below. Yield (y kg) Freque
June 2013, Legacy S1 (01R), Q4 (10 marks): The time, in minutes, taken to fly from London to Malaga has a normal distribution with mean 150 minutes and standard deviation 10 minutes. (a) Find the probabi
June 2013, Legacy S1 (01R), Q5 (11 marks): A researcher believes that parents with a short family name tended to give their children a long first name. A random sample of 10 children was selected and the
June 2013, Legacy S1 (01R), Q6 (9 marks): Figure 1 The Venn diagram in Figure 1 shows three events A, B and C and the probabilities associated with each region of B. The constants p, q and r each repres
June 2013, Legacy S1 (01R), Q7 (18 marks): The score S when a spinner is spun has the following probability distribution. s 0 1 2 4 5 P(S = s) 0.2 0.2 0.1 0.3 0.2 (a) Find E(S). (2) (b) Show that E(S 2)
January 2013, Legacy S1, Q1 (7 marks): A teacher asked a random sample of 10 students to record the number of hours of television, t, they watched in the week before their mock exam. She then calcula
January 2013, Legacy S1, Q2 (8 marks): The discrete random variable X can take only the values 1, 2 and 3. For these values the cumulative distribution function is defined by F( ) , , x x k x = + = 3
January 2013, Legacy S1, Q3 (10 marks): A biologist is comparing the intervals (m seconds) between the mating calls of a certain species of tree frog and the surrounding temperature (t °C). The follow
January 2013, Legacy S1, Q4 (10 marks): The length of time, L hours, that a phone will work before it needs charging is normally distributed with a mean of 100 hours and a standard deviation of 15 hou
January 2013, Legacy S1, Q5 (15 marks): A survey of 100 households gave the following results for weekly income £y. Income y (£) Mid-point Frequency f 0 y < 200 100 12 200 y < 240 220 28 240 y <
January 2013, Legacy S1, Q6 (13 marks): A fair blue die has faces numbered 1, 1, 3, 3, 5 and 5. The random variable B represents the score when the blue die is rolled. (a) Write down the probability d
January 2013, Legacy S1, Q7 (12 marks): Given that P(A) = 0.35 , P(B) = 0.45 and P(A B find (a) P(A B) (2) (b) P() (2) The event C has P(C) = 0.20 The events A and C are mutually exclu
June 2012, Legacy S1, Q1 (10 marks): A discrete random variable X has the probability function and 2 otherwise ( ) , , k x x − = − 1 1 0 1 0 2 { P ( ) X x = = (a) Show that k = 1 6 (3) (b) Find E(X
June 2012, Legacy S1, Q2 (6 marks): A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, u, and how many have had their house reposse
June 2012, Legacy S1, Q3 (15 marks): A scientist is researching whether or not birds of prey exposed to pollutants lay eggs with thinner shells. He collects a random sample of egg shells from each
June 2012, Legacy S1, Q4 (9 marks): B T W 4 5 3 7 6 Figure 1 Figure 1 shows how 25 people travelled to work. Their travel to work is represented by the events B bicycle T train W walk (a) Write do
June 2012, Legacy S1, Q5 (13 marks): 0 5 10 15 20 25 30 35 40 45 50 Frequency density Speed of car Figure 2 A policeman records the speed of the traffic on a busy road with a 30 mph speed limit. He
June 2012, Legacy S1, Q6 (10 marks): The heights of an adult female population are normally distributed with mean 162 cm and standard deviation 7.5 cm. (a) Find the probability that a randomly chos
June 2012, Legacy S1, Q7 (12 marks): A manufacturer carried out a survey of the defects in their soft toys. It is found that the probability of a toy having poor stitching is 0.03 and that a toy wi
January 2012, Legacy S1, Q1 (4 marks): The histogram in Figure 1 shows the time, to the nearest minute, that a random sample of 100 motorists were delayed by roadworks on a stretch of motorway. 0 5 1
January 2012, Legacy S1, Q2 (9 marks): (a) State in words the relationship between two events R and S when P( ) R S ∩ = 0 (1) The events A and B are independent with P(A) = 4 1 and P( ) A B ∪ = 3 2 F
January 2012, Legacy S1, Q3 (11 marks): The discrete random variable X can take only the values 2, 3, 4 or 6. For these values the probability distribution function is given by x 2 3 4 6 P(X = x) 5 21
January 2012, Legacy S1, Q4 (13 marks): The marks, x, of 45 students randomly selected from those students who sat a mathematics examination are shown in the stem and leaf diagram below. Mark Totals 3
January 2012, Legacy S1, Q5 (15 marks): The age, t years, and weight, w grams, of each of 10 coins were recorded. These data are summarised below. t2 = 2688 tw = 1760.62 t = 158 w = 111.75 Sww
January 2012, Legacy S1, Q6 (13 marks): The following shows the results of a survey on the types of exercise taken by a group of 100 people. 65 run 48 swim 60 cycle 40 run and swim 30 swim and cycle 3
January 2012, Legacy S1, Q7 (10 marks): A manufacturer fills jars with coffee. The weight of coffee, W grams, in a jar can be modelled by a normal distribution with mean 232 grams and standard deviati
June 2011, Legacy S1, Q1 (7 marks): On a particular day the height above sea level, x metres, and the mid-day temperature, y°C, were recorded in 8 north European towns. These data are summarised b
June 2011, Legacy S1, Q2 (5 marks): The random variable X ~ ( , ) N μ 52 and P( 23) 0.9192 X = (a) Find the value of (μ. (4) (b) Write down the value of P( ). μ < < X 23 (1)
June 2011, Legacy S1, Q3 (7 marks): The discrete random variable Y has probability distribution y 1 2 3 4 P(Y = y) a b 0.3 c where a, b and c are constants. The cumulative distribution function F(
June 2011, Legacy S1, Q4 (7 marks): Past records show that the times, in seconds, taken to run 100 m by children at a school can be modelled by a normal distribution with a mean of 16.12 and a sta
June 2011, Legacy S1, Q5 (11 marks): A class of students had a sudoku competition. The time taken for each student to complete the sudoku was recorded to the nearest minute and the results are summ
June 2011, Legacy S1, Q6 (9 marks): Jake and Kamil are sometimes late for school. The events J and K are defined as follows J = the event that Jake is late for school K = the event that Kamil is l
June 2011, Legacy S1, Q7 (12 marks): A teacher took a random sample of 8 children from a class. For each child the teacher recorded the length of their left foot, f cm, and their height, h cm. The
June 2011, Legacy S1, Q8 (17 marks): A spinner is designed so that the score S is given by the following probability distribution. s 0 1 2 4 5 P(S = s) p 0.25 0.25 0.20 0.20 (a) Find the value of p
January 2011, Legacy S1, Q1 (6 marks): A random sample of 50 salmon was caught by a scientist. He recorded the length l cm and weight w kg of each salmon. The following summary statistics were calcul
January 2011, Legacy S1, Q2 (4 marks): Keith records the amount of rainfall, in mm, at his school, each day for a week. The results are given below. 2.8 5.6 2.3 9.4 0.0 0.5 1.8 Jenny then records the
January 2011, Legacy S1, Q3 (9 marks): Over a long period of time a small company recorded the amount it received in sales per month. The results are summarised below. Amount received in sales (£1000
January 2011, Legacy S1, Q4 (6 marks): A farmer collected data on the annual rainfall, x cm, and the annual yield of peas, p tonnes per acre. The data for annual rainfall was coded using v = 5 10 x −
January 2011, Legacy S1, Q5 (7 marks): On a randomly chosen day, each of the 32 students in a class recorded the time, t minutes to the nearest minute, they spent on their homework. The data for the
January 2011, Legacy S1, Q6 (14 marks): The discrete random variable X has the probability distribution x 1 2 3 4 P(X = x) k 2k 3k 4k (a) Show that k = 0.1 (1) Find (b) E(X) (2) (c) E(X 2) (2) (d) Var
January 2011, Legacy S1, Q7 (17 marks): The bag P contains 6 balls of which 3 are red and 3 are yellow. The bag Q contains 7 balls of which 4 are red and 3 are yellow. A ball is drawn at random from b
January 2011, Legacy S1, Q8 (12 marks): The weight, X grams, of soup put in a tin by machine A is normally distributed with a mean of 160 g and a standard deviation of 5 g. A tin is selected at random
June 2010, Legacy S1, Q1 (4 marks): Gary compared the total attendance, x, at home matches and the total number of goals, y, scored at home during a season for each of 12 football teams playing in
June 2010, Legacy S1, Q2 (10 marks): An experiment consists of selecting a ball from a bag and spinning a coin. The bag contains 5 red balls and 7 blue balls. A ball is selected at random from the
June 2010, Legacy S1, Q3 (11 marks): The discrete random variable X has probability distribution given by x 1 − 0 1 2 3 P( ) X x = 1 5 a 1 10 a 1 5 where a is a constant. (a) Find the value of a. (
June 2010, Legacy S1, Q4 (10 marks): The Venn diagram in Figure 1 shows the number of students in a class who read any of 3 popular magazines A, B and C. Figure 1 One of these students is selected
June 2010, Legacy S1, Q5 (14 marks): A teacher selects a random sample of 56 students and records, to the nearest hour, the time spent watching television in a particular week. Hours 1 10 − 11 20 −
June 2010, Legacy S1, Q6 (14 marks): A travel agent sells flights to different destinations from Beerow airport. The distance d, measured in 100 km, of the destination from the airport and the fare
June 2010, Legacy S1, Q7 (12 marks): The distances travelled to work, D km, by the employees at a large company are normally distributed with D ∼N( , ). 30 82 (a) Find the probability that a random
January 2010, Legacy S1, Q1 (5 marks): A jar contains 2 red, 1 blue and 1 green bead. Two beads are drawn at random from the jar without replacement. (a) In the space below, draw a tree diagram to il
January 2010, Legacy S1, Q2 (9 marks): The 19 employees of a company take an aptitude test. The scores out of 40 are illustrated in the stem and leaf diagram below. 2|6 means a score of 26 0 7 (1) 1
January 2010, Legacy S1, Q3 (11 marks): The birth weights, in kg, of 1500 babies are summarised in the table below. Weight (kg) Midpoint, xkg Frequency, f 0.0 – 1.0 0.50 1 1.0 – 2.0 1.50 6 2.0 – 2.5 2
January 2010, Legacy S1, Q4 (9 marks): There are 180 students at a college following a general course in computing. Students on this course can choose to take up to three extra options. 112 take syst
January 2010, Legacy S1, Q5 (10 marks): The probability function of a discrete random variable X is given by 2 p( ) 1,2,3 x kx x = = where k is a positive constant. (a) Show that 1 14 k = (2) Find (b)
January 2010, Legacy S1, Q6 (18 marks): The blood pressures, p mmHg, and the ages, t years, of 7 hospital patients are shown in the table below. Patient A B C D E F G t 42 74 48 35 56 26 60 p 98 130 1
January 2010, Legacy S1, Q7 (13 marks): The heights of a population of women are normally distributed with mean μ cm and standard deviation σ cm. It is known that 30% of the women are taller than 172

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