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CAIE S1 2019 June Q4
5 marks Standard +0.3
4 It is known that 20\% of male giant pandas in a certain area weigh more than 121 kg and \(71.9 \%\) weigh more than 102 kg . Weights of male giant pandas in this area have a normal distribution. Find the mean and standard deviation of the weights of male giant pandas in this area.
CAIE S1 2019 June Q5
11 marks Moderate -0.8
5 Maryam has 7 sweets in a tin; 6 are toffees and 1 is a chocolate. She chooses one sweet at random and takes it out. Her friend adds 3 chocolates to the tin. Then Maryam takes another sweet at random out of the tin.
  1. Draw a fully labelled tree diagram to illustrate this situation.
  2. Draw up the probability distribution table for the number of toffees taken.
  3. Find the mean number of toffees taken.
  4. Find the probability that the first sweet taken is a chocolate, given that the second sweet taken is a toffee.
CAIE S1 2019 June Q6
10 marks Easy -1.8
6
  1. Give one advantage and one disadvantage of using a box-and-whisker plot to represent a set of data.
  2. The times in minutes taken to run a marathon were recorded for a group of 13 marathon runners and were found to be as follows. $$\begin{array} { l l l l l l l l l l l l l } 180 & 275 & 235 & 242 & 311 & 194 & 246 & 229 & 238 & 768 & 332 & 227 & 228 \end{array}$$ State which of the mean, mode or median is most suitable as a measure of central tendency for these times. Explain why the other measures are less suitable.
  3. Another group of 33 people ran the same marathon and their times in minutes were as follows.
    190203215246249253255254258260261
    263267269274276280288283287294300
    307318327331336345351353360368375
    (a) On the grid below, draw a box-and-whisker plot to illustrate the times for these 33 people. \includegraphics[max width=\textwidth, alt={}, center]{f4d040a2-6a04-49ce-98ac-8ba5c515f905-09_611_1202_1270_555}
    (b) Find the interquartile range of these times.
CAIE S1 2019 June Q7
10 marks Standard +0.3
7
  1. A group of 6 teenagers go boating. There are three boats available. One boat has room for 3 people, one has room for 2 people and one has room for 1 person. Find the number of different ways the group of 6 teenagers can be divided between the three boats.
  2. Find the number of different 7-digit numbers which can be formed from the seven digits 2, 2, 3, 7, 7, 7, 8 in each of the following cases.
    1. The odd digits are together and the even digits are together.
    2. The 2 s are not together.
      If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
CAIE S1 2019 June Q1
6 marks Moderate -0.8
1 The time taken, in minutes, by a ferry to cross a lake has a normal distribution with mean 85 and standard deviation 6.8.
  1. Find the probability that, on a randomly chosen occasion, the time taken by the ferry to cross the lake is between 79 and 91 minutes.
  2. Over a long period it is found that \(96 \%\) of ferry crossings take longer than a certain time \(t\) minutes. Find the value of \(t\).
CAIE S1 2019 June Q2
6 marks Moderate -0.3
2 Megan sends messages to her friends in one of 3 different ways: text, email or social media. For each message, the probability that she uses text is 0.3 and the probability that she uses email is 0.2 . She receives an immediate reply from a text message with probability 0.4 , from an email with probability 0.15 and from social media with probability 0.6 .
  1. Draw a fully labelled tree diagram to represent this information.
  2. Given that Megan does not receive an immediate reply to a message, find the probability that the message was an email.
CAIE S1 2019 June Q3
5 marks Moderate -0.8
3 Mr and Mrs Keene and their 5 children all go to watch a football match, together with their friends Mr and Mrs Uzuma and their 2 children. Find the number of ways in which all 11 people can line up at the entrance in each of the following cases.
  1. Mr Keene stands at one end of the line and Mr Uzuma stands at the other end.
  2. The 5 Keene children all stand together and the Uzuma children both stand together.
CAIE S1 2019 June Q4
6 marks Standard +0.3
4
  1. Find the number of ways a committee of 6 people can be chosen from 8 men and 4 women if there must be at least twice as many men as there are women on the committee.
  2. Find the number of ways a committee of 6 people can be chosen from 8 men and 4 women if 2 particular men refuse to be on the committee together.
CAIE S1 2019 June Q5
8 marks Standard +0.3
5 On average, \(34 \%\) of the people who go to a particular theatre are men.
  1. A random sample of 14 people who go to the theatre is chosen. Find the probability that at most 2 people are men.
  2. Use an approximation to find the probability that, in a random sample of 600 people who go to the theatre, fewer than 190 are men.
CAIE S1 2019 June Q6
9 marks Moderate -0.8
6 A fair five-sided spinner has sides numbered 1, 1, 1, 2, 3. A fair three-sided spinner has sides numbered \(1,2,3\). Both spinners are spun once and the score is the product of the numbers on the sides the spinners land on.
  1. Draw up the probability distribution table for the score. \includegraphics[max width=\textwidth, alt={}, center]{da4a61b9-f55d-40ed-a721-a6aee962f0d6-08_67_1569_484_328}
  2. Find the mean and the variance of the score.
  3. Find the probability that the score is greater than the mean score.
CAIE S1 2019 June Q7
10 marks Easy -1.2
7 The times in minutes taken by 13 pupils at each of two schools in a cross-country race are recorded in the table below.
Thaters School38434852545657585861626675
Whitefay Park School45475356566164666973757883
  1. Draw a back-to-back stem-and-leaf diagram to illustrate these times with Thaters School on the left.
  2. Find the interquartile range of the times for pupils at Thaters School.
    The times taken by pupils at Whitefay Park School are denoted by \(x\) minutes.
  3. Find the value of \(\Sigma ( x - 60 ) ^ { 2 }\).
  4. It is given that \(\Sigma ( x - 60 ) = 46\). Use this result, together with your answer to part (iii), to find the variance of \(x\).
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.
CAIE S1 2016 March Q1
3 marks Easy -1.8
1 For 10 values of \(x\) the mean is 86.2 and \(\Sigma ( x - a ) = 362\). Find the value of
  1. \(\Sigma x\),
  2. the constant \(a\).
CAIE S1 2016 March Q2
4 marks Moderate -0.8
2 A flower shop has 5 yellow roses, 3 red roses and 2 white roses. Martin chooses 3 roses at random. Draw up the probability distribution table for the number of white roses Martin chooses.
CAIE S1 2016 March Q3
7 marks Standard +0.3
3 A fair eight-sided die has faces marked \(1,2,3,4,5,6,7,8\). The score when the die is thrown is the number on the face the die lands on. The die is thrown twice.
  • Event \(R\) is 'one of the scores is exactly 3 greater than the other score'.
  • Event \(S\) is 'the product of the scores is more than 19'.
    1. Find the probability of \(R\).
    2. Find the probability of \(S\).
    3. Determine whether events \(R\) and \(S\) are independent. Justify your answer.
CAIE S1 2016 March Q4
7 marks Moderate -0.8
4 A survey was made of the journey times of 63 people who cycle to work in a certain town. The results are summarised in the following cumulative frequency table.
Journey time (minutes)\(\leqslant 10\)\(\leqslant 25\)\(\leqslant 45\)\(\leqslant 60\)\(\leqslant 80\)
Cumulative frequency018505963
  1. State how many journey times were between 25 and 45 minutes.
  2. Draw a histogram on graph paper to represent the data.
  3. Calculate an estimate of the mean journey time.
CAIE S1 2016 March Q5
8 marks Moderate -0.3
5 In a certain town, 35\% of the people take a holiday abroad and 65\% take a holiday in their own country. Of those going abroad \(80 \%\) go to the seaside, \(15 \%\) go camping and \(5 \%\) take a city break. Of those taking a holiday in their own country, \(20 \%\) go to the seaside and the rest are divided equally between camping and a city break.
  1. A person is chosen at random. Given that the person chosen goes camping, find the probability that the person goes abroad.
  2. A group of \(n\) people is chosen randomly. The probability of all the people in the group taking a holiday in their own country is less than 0.002 . Find the smallest possible value of \(n\).
CAIE S1 2016 March Q6
10 marks Moderate -0.8
6 Hannah chooses 5 singers from 15 applicants to appear in a concert. She lists the 5 singers in the order in which they will perform.
  1. How many different lists can Hannah make? Of the 15 applicants, 10 are female and 5 are male.
  2. Find the number of lists in which the first performer is male, the second is female, the third is male, the fourth is female and the fifth is male. Hannah's friend Ami would like the group of 5 performers to include more males than females. The order in which they perform is no longer relevant.
  3. Find the number of different selections of 5 performers with more males than females.
  4. Two of the applicants are Mr and Mrs Blake. Find the number of different selections that include Mr and Mrs Blake and also fulfil Ami's requirement.
CAIE S1 2016 March Q7
11 marks Standard +0.3
7 The times taken by a garage to fit a tow bar onto a car have a normal distribution with mean \(m\) hours and standard deviation 0.35 hours. It is found that \(95 \%\) of times taken are longer than 0.9 hours.
  1. Find the value of \(m\).
  2. On one day 4 cars have a tow bar fitted. Find the probability that none of them takes more than 2 hours to fit. The times in hours taken by another garage to fit a tow bar onto a car have the distribution \(\mathrm { N } \left( \mu , \sigma ^ { 2 } \right)\) where \(\mu = 3 \sigma\).
  3. Find the probability that it takes more than \(0.6 \mu\) hours to fit a tow bar onto a randomly chosen car at this garage.
CAIE S1 2017 March Q1
4 marks Easy -1.2
1 Twelve values of \(x\) are shown below.
1761.61758.51762.31761.41759.41759.1
1762.51761.91762.41761.91762.81761.0
Find the mean and standard deviation of \(( x - 1760 )\). Hence find the mean and standard deviation of \(x\). [4]
CAIE S1 2017 March Q2
3 marks Moderate -0.5
2 A bag contains 10 pink balloons, 9 yellow balloons, 12 green balloons and 9 white balloons. 7 balloons are selected at random without replacement. Find the probability that exactly 3 of them are green.
CAIE S1 2017 March Q3
5 marks Moderate -0.3
3 It is found that \(10 \%\) of the population enjoy watching Historical Drama on television. Use an appropriate approximation to find the probability that, out of 160 people chosen randomly, more than 17 people enjoy watching Historical Drama on television.
CAIE S1 2017 March Q4
7 marks Easy -1.8
4 The weights in kilograms of packets of cereal were noted correct to 4 significant figures. The following stem-and-leaf diagram shows the data.
7473\(( 1 )\)
748125779\(( 6 )\)
749022235556789\(( 12 )\)
750112223445677889\(( 15 )\)
7510023344455779\(( 13 )\)
75200011223444\(( 11 )\)
7532\(( 1 )\)
Key: 748 | 5 represents 0.7485 kg .
  1. On the grid, draw a box-and-whisker plot to represent the data. \includegraphics[max width=\textwidth, alt={}, center]{556a1cc2-47ef-4ef7-a8f6-42850c303531-05_814_1604_1336_299}
  2. Name a distribution that might be a suitable model for the weights of this type of cereal packet. Justify your answer.
CAIE S1 2017 March Q5
9 marks Standard +0.3
5
  1. A plate of cakes holds 12 different cakes. Find the number of ways these cakes can be shared between Alex and James if each receives an odd number of cakes.
  2. Another plate holds 7 cup cakes, each with a different colour icing, and 4 brownies, each of a different size. Find the number of different ways these 11 cakes can be arranged in a row if no brownie is next to another brownie.
  3. A plate of biscuits holds 4 identical chocolate biscuits, 6 identical shortbread biscuits and 2 identical gingerbread biscuits. These biscuits are all placed in a row. Find how many different arrangements are possible if the chocolate biscuits are all kept together.
CAIE S1 2017 March Q6
9 marks Moderate -0.3
6 Pack \(A\) consists of ten cards numbered \(0,0,1,1,1,1,1,3,3,3\). Pack \(B\) consists of six cards numbered \(0,0,2,2,2,2\). One card is chosen at random from each pack. The random variable \(X\) is defined as the sum of the two numbers on the cards.
  1. Show that \(\mathrm { P } ( X = 2 ) = \frac { 2 } { 15 }\). \includegraphics[max width=\textwidth, alt={}, center]{556a1cc2-47ef-4ef7-a8f6-42850c303531-08_59_1569_497_328}
  2. Draw up the probability distribution table for \(X\).
  3. Given that \(X = 3\), find the probability that the card chosen from pack \(A\) is a 1 .
CAIE S1 2017 March Q7
13 marks Standard +0.3
7
  1. The lengths, in centimetres, of middle fingers of women in Raneland have a normal distribution with mean \(\mu\) and standard deviation \(\sigma\). It is found that \(25 \%\) of these women have fingers longer than 8.8 cm and \(17.5 \%\) have fingers shorter than 7.7 cm .
    1. Find the values of \(\mu\) and \(\sigma\).
      The lengths, in centimetres, of middle fingers of women in Snoland have a normal distribution with mean 7.9 and standard deviation 0.44. A random sample of 5 women from Snoland is chosen.
    2. Find the probability that exactly 3 of these women have middle fingers shorter than 8.2 cm .
  2. The random variable \(X\) has a normal distribution with mean equal to the standard deviation. Find the probability that a particular value of \(X\) is less than 1.5 times the mean.