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OCR MEI Further Statistics A AS 2019 June Q4
8 marks Moderate -0.3
4 A student is investigating correlations between various personality traits, two of which are conscientiousness and openness to new experiences.
She selects a random sample of 10 students at her university and uses standard tests to measure their conscientiousness and their openness. The product moment correlation coefficient between these two variables for the 10 students is 0.476 .
  1. Assuming that the underlying population has a bivariate Normal distribution, carry out a hypothesis test at the \(10 \%\) significance level to investigate whether there is any correlation between openness and conscientiousness in students. Table 4.1 below shows the values of the product moment correlation coefficients between 5 different personality traits for a much larger sample of students. Those correlations that are significant at the \(5 \%\) level are denoted by a * after the value of the correlation. \begin{table}[h]
    NeuroticismExtroversionOpennessAgreeablenessConscientiousness
    Neuroticism1
    Extroversion-0.296*1
    Openness-0.0440.405*1
    Agreeableness-0.190*0.0610.0421
    Conscientiousness-0.485*0.1450.235*0.1121
    \captionsetup{labelformat=empty} \caption{Table 4.1}
    \end{table} The student analyses these factors for effect size.
    Guidelines often used when considering effect size are given in Table 4.2 below. \begin{table}[h]
    Product moment
    correlation coefficient
    		Effect size
    0.1Small
    0.3Medium
    0.5Large
    \captionsetup{labelformat=empty} \caption{Table 4.2}
    \end{table}
  2. The student notes that, despite the result of the test in part (a), the correlation between openness and conscientiousness is significant at the \(5 \%\) level with this second sample. Comment briefly on why this may be the case.
  3. The student intends to summarise her findings about relationships between these factors, including effect sizes, in a report.
    Use the information in Tables 4.1 and 4.2 to identify two summary points the student could make.
OCR MEI Further Statistics A AS 2019 June Q5
13 marks Standard +0.3
5 A researcher is investigating births of females and males in a particular species of animal which very often produces litters of 7 offspring.
The table shows some data about the number of females per litter in 200 litters of 7 offspring. The researcher thinks that a binomial distribution \(\mathrm { B } ( 7 , p )\) may be an appropriate model for these data. (c) Complete the test at the \(5 \%\) significance level. Fig. 5 shows the probability distribution \(\mathrm { B } ( 7,0.35 )\) together with the relative frequencies of the observed data (the numbers of litters each divided by 200). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fd496303-10f1-450e-bbeb-421ab6f4de21-5_659_1285_342_319} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure} (d) Comment on the result of the test completed in part (c) by considering Fig. 5.
OCR MEI Further Statistics A AS 2019 June Q6
13 marks Standard +0.3
6 A meteorologist is investigating the relationship between altitude \(x\) metres and mean annual temperature \(y ^ { \circ } \mathrm { C }\) in an American state.
She selects 12 locations at various altitudes and then stations a remote monitoring device at each of them to measure the temperature over the course of a year. Fig. 6 illustrates the data which she obtains. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{fd496303-10f1-450e-bbeb-421ab6f4de21-6_686_1477_486_292} \captionsetup{labelformat=empty} \caption{Fig. 6}
\end{figure}
  1. Explain why it would not be appropriate to carry out a hypothesis test for correlation based on the product moment correlation coefficient.
  2. Explain why altitude has been plotted on the horizontal axis in Fig. 6. Summary statistics for \(x\) and \(y\) are as follows. $$\sum x = 21200 \quad \sum y = 105.4 \quad \sum x ^ { 2 } = 39100000 \quad \sum y ^ { 2 } = 1004 \quad \sum x y = 176090$$
  3. Calculate the equation of the regression line of \(y\) on \(x\).
  4. Use the equation of the regression line to predict the values of the mean annual temperature at each of the following altitudes.
OCR MEI Further Statistics A AS 2022 June Q1
6 marks Moderate -0.3
1 A fair five-sided spinner has sectors labelled 1, 2, 3, 4, 5. In a game at a stall at a charity event, the spinner is spun twice. The random variable \(X\) represents the lower of the two scores. The probability distribution of \(X\) is given by the formula \(\mathrm { P } ( \mathrm { X } = \mathrm { r } ) = \mathrm { k } ( 11 - 2 \mathrm { r } )\) for \(r = 1,2,3,4,5\),
where \(k\) is a constant.
  1. Complete the copy of this table in the Printed Answer Booklet.
    \(r\)12345
    \(\mathrm { P } ( X = r )\)\(7 k\)\(3 k\)
  2. Determine the value of \(k\).
  3. Find each of the following.
    Given that the average profit that the stall-holder makes on one game is 25 pence, find the value of \(C\).
OCR MEI Further Statistics A AS 2022 June Q2
7 marks Easy -1.2
2 On a car assembly line, a robot is used for a particular task.
  1. State the conditions under which a Poisson distribution is an appropriate model for the number of breakdowns of the robot in a week. It is given that the average number of breakdowns of the robot in a week is 1.7 . For the remainder of this question, you should assume that a Poisson distribution is an appropriate model for the number of breakdowns of the robot in a week.
    1. Find the probability that the number of breakdowns of the robot in a week is exactly 4.
    2. Determine the probability that the number of breakdowns of the robot in a week is at least 2 .
  3. Determine the probability that the number of breakdowns of the robot in 52 weeks is less than 100.
OCR MEI Further Statistics A AS 2022 June Q3
10 marks Standard +0.3
3 A biology student is doing an experiment in which plants are inoculated with a particular microorganism in an attempt to help them grow. She is investigating whether there is any association between the percentage of roots which have been colonised by the microorganism and the dry weight of the plant shoots. After the plants have grown for a few weeks, the student takes a random sample of 10 plants and measures the percentage of roots which have been colonised by the microorganism and the dry weight of the plant shoots. The spreadsheet output shows the data, together with a scatter diagram to illustrate the data. \includegraphics[max width=\textwidth, alt={}, center]{8f1e0c68-a334-4657-823e-386ab0994c02-3_722_1648_635_244}
  1. The student decides that a test based on Pearson's product moment correlation coefficient may not be valid. Explain why she comes to this conclusion.
  2. Calculate the value of Spearman's rank correlation coefficient.
  3. Carry out a test based on this coefficient, at the \(5 \%\) significance level, to investigate whether there is any association between percentage colonisation and shoot dry weight.
OCR MEI Further Statistics A AS 2022 June Q4
6 marks Moderate -0.8
4 A random number generator generates integers between 1 and 50 inclusive, with each number having an equal probability of being generated.
  1. State the probability distribution of the numbers generated.
  2. Determine the probability that a number generated is within one standard deviation of the mean.
OCR MEI Further Statistics A AS 2022 June Q5
14 marks Standard +0.3
5 A researcher is investigating whether there is any relationship between the overall performance of a student at GCSE and their grade in A Level Mathematics. Their A Level Mathematics grade is classified as A* or A, B, C or lower, and their overall performance at GCSE is classified as Low, Middle, High. Data are collected for a sample of 80 students in a particular area. The researcher carries out a chi-squared test. The screenshot below shows part of a spreadsheet used to analyse the data. Some values in the spreadsheet have been deliberately omitted.
1ABCDE
\multirow{2}{*}{
}Observed frequency
A* or ABC or lowerTotals
3Low613928
4Middle106824
5High1510328
6Totals31292080
7
8\multirow{2}{*}{}
9A* or ABC or lower
10Low10.85
11Middle9.30
12High10.85
13\multirow[b]{2}{*}{Contribution to the test statistic}
14
15A* or ABC or lower
16Low2.16800.80020.5714
17Middle0.05270.83790.6667
18High1.5873
2.2857
2.2857
19
  1. State what needs to be known about the sample for the test to be valid. For the remainder of this question, you should assume that the test is valid.
  2. Determine the missing values in each of the following cells.
    Carry out a hypothesis test at the \(10 \%\) significance level to investigate whether there is any association between level of performance at GCSE and A Level Mathematics grade.
  3. Discuss briefly what the data suggest about A Level Mathematics grade for different levels of performance at GCSE.
  4. State one disadvantage of using a 10\% significance level rather than a 5\% significance level in a hypothesis test.
OCR MEI Further Statistics A AS 2022 June Q6
10 marks Moderate -0.8
6 Tom has read in a newspaper that you can tell the air temperature by counting how often a cricket chirps in a period of 20 seconds. (A cricket is a type of insect.) He wants to know exactly how the temperature can be predicted. On 8 randomly selected days, when Tom can hear crickets chirping, he records the number of chirps, \(x\), made by a cricket in a 20-second interval, and also the temperature, \(y ^ { \circ } \mathrm { C }\), at that time. The data are summarised as follows. \(n = 8 \quad \sum x = 268 \quad \sum y = 141.9 \quad \sum x ^ { 2 } = 9618 \quad \sum y ^ { 2 } = 2630.55 \quad \sum \mathrm { xy } = 5009.1\) These data are illustrated below. \includegraphics[max width=\textwidth, alt={}, center]{8f1e0c68-a334-4657-823e-386ab0994c02-5_661_1035_699_242}
  1. Determine the equation of the regression line of \(y\) on \(x\). Give your answer in the form \(\mathrm { y } = \mathrm { ax } + \mathrm { b }\), giving the values of \(a\) and \(b\) correct to \(\mathbf { 3 }\) significant figures.
  2. Use the equation of the regression line to predict the temperature for the following values of \(x\).
OCR MEI Further Statistics A AS 2022 June Q7
7 marks Moderate -0.8
7 On average one in five packets of a breakfast cereal contains a voucher for a discount on the next packet bought. Whether or not a packet contains a voucher is independent of other packets, and can only be determined by opening the packet.
  1. State the distribution of the number of packets that need to be opened in order to find one which contains a voucher.
  2. Determine the probability that exactly 4 packets have to be opened in order to find one which contains a voucher.
  3. Determine the probability that exactly 10 packets have to be opened in order to find two which contain a voucher.
  4. I have \(n\) packets, and I open them one by one until I find a voucher or until all the packets are open. Given that the probability that I find a voucher is greater than 0.99 , determine the least possible value of \(n\).
OCR MEI Further Statistics A AS 2023 June Q1
12 marks Moderate -0.3
1 Ryan has 6 one-pound coins and 4 two-pound coins. Ryan decides to select 3 of these coins at random to donate to a charity. The total value, in pounds, of these 3 coins is denoted by the random variable \(X\).
  1. Show that \(\mathrm { P } ( X = 3 ) = \frac { 1 } { 6 }\). The table below shows the probability distribution of \(X\).
    \(r\)3456
    \(\mathrm { P } ( \mathrm { X } = \mathrm { r } )\)\(\frac { 1 } { 6 }\)\(\frac { 1 } { 2 }\)\(\frac { 3 } { 10 }\)\(\frac { 1 } { 30 }\)
  2. Draw a graph to illustrate the distribution.
  3. In this question you must show detailed reasoning. Find each of the following.
    Ryan's friend Sasha decides to give the same amount as Ryan does to the charity plus an extra three pounds. The random variable \(Y\) represents the total amount of money, in pounds, given by Ryan and Sasha.
  4. Determine each of the following.
OCR MEI Further Statistics A AS 2023 June Q2
6 marks Easy -1.2
2 A group of friends live by the sea. Each day they look out to sea in the hope of seeing a dolphin. The probability that they see a dolphin on any day is 0.15 . You should assume that this probability is not affected by whether or not they see a dolphin on any other day.
  1. Explain why you can use a geometric distribution to model the number of days that it takes for them to first see a dolphin.
  2. Find the probability that they see a dolphin for the first time on the fifth day.
  3. Find the probability that they do not see a dolphin for at least 10 days.
  4. Determine the mean and the variance of the number of days that it takes for them to see a dolphin.
OCR MEI Further Statistics A AS 2023 June Q3
7 marks Moderate -0.8
3 At a pottery which manufactures mugs, it is known that \(5 \%\) of mugs are faulty. The mugs are produced in batches of 20 . Faults are modelled as occurring randomly and independently. The number of faulty mugs in a batch is denoted by the random variable \(X\).
  1. Determine \(\mathrm { P } ( X \geqslant 2 )\).
  2. Find \(\operatorname { Var } ( X )\). Independently of the mugs, the pottery also manufactures cups, and it is known that \(7 \%\) of cups are faulty. The cups are produced in batches of 30 . Faults are modelled as occurring randomly and independently. The number of faulty cups in a batch is denoted by the random variable \(Y\).
  3. Determine the standard deviation of \(X + Y\). When 10 batches of cups have been produced, a sample of 15 cups is tested to ensure that the handles of the cups are properly attached.
  4. Explain why it might not be sensible to select a sample of 15 cups from the same batch.
OCR MEI Further Statistics A AS 2023 June Q4
10 marks Standard +0.3
4 At a parcel delivery company it is known that the probability that a parcel is delivered to the wrong address is 0.0005 . On a particular day, 15000 parcels are delivered. The number of parcels delivered to the wrong address is denoted by the random variable \(X\).
  1. Explain why the binomial distribution and the Poisson distribution could both be suitable models for the distribution of \(X\).
  2. Use a Poisson distribution to find each of the following.
    • \(\mathrm { P } ( X = 5 )\)
    • \(\mathrm { P } ( X \geqslant 8 )\)
    You are given that 15000 parcels are delivered each day in a 5-day working week.
    1. Determine the probability that at least 40 parcels are delivered to the wrong address during the week.
    2. Determine the probability that at least 8 parcels are delivered to the wrong address on each of the 5 days in the week.
OCR MEI Further Statistics A AS 2023 June Q5
10 marks Standard +0.3
5 Two practice GCSE examinations in mathematics are given to all of the students in a large year group. A teacher wants to check whether there is a positive relationship between the marks obtained by the students in the two examinations. She selects a random sample of 20 students. Summary data for the marks obtained in the first and second practice examinations, \(x\) and \(y\) respectively, are as follows. $$\sum x = 565 \quad \sum y = 724 \quad \sum x ^ { 2 } = 17103 \quad \sum y ^ { 2 } = 29286 \quad \sum x y = 21635$$ The teacher decides to carry out a hypothesis test based on Pearson's product moment correlation coefficient.
  1. In this question you must show detailed reasoning. Calculate the value of Pearson's product moment correlation coefficient.
  2. Carry out the test at the \(5 \%\) significance level.
  3. Given that the teacher did not draw a scatter diagram before carrying out the test, comment on the validity of the test.
OCR MEI Further Statistics A AS 2023 June Q6
15 marks Standard +0.3
6 An eight-sided dice has its faces numbered \(1,2 , \ldots , 8\). \begin{enumerate}[label=(\alph*)] \item In this part of the question you should assume that the dice is fair.
  1. State the probability that, when the dice is rolled once, the score is at least 6 .
  2. Show that the probability that the score is within 2 standard deviations of its mean is 1 .
\item A student thinks that the dice may be biased. To investigate this, the student decides to roll the dice 80 times and then carry out a \(\chi ^ { 2 }\) goodness of fit test of a uniform distribution. The spreadsheet below shows the data for the test, where some of the values have been deliberately omitted.
\multirow[b]{2}{*}{1}ABCD
ScoreObserved frequencyExpected frequencyChi-squared contribution
2114101.6
324103.6
4310100
541510
656101.6
7611100.1
877100.9
98100.9
  1. Explain why all of the expected frequencies are equal to 10 .
  2. Determine the missing values in each of the following cells.
    Carry out the \(\chi ^ { 2 }\) test at the \(5 \%\) significance level.
OCR MEI Further Statistics A AS 2024 June Q1
7 marks Easy -1.2
1 The probability distribution for a discrete random variable \(X\) is given in the table below.
\(x\)0123
\(\mathrm { P } ( \mathrm { X } = \mathrm { x } )\)\(2 c\)\(3 c\)\(0.5 - c\)\(c\)
  1. Find the value of \(c\).
  2. Find the value of each of the following.
    The random variable \(Y\) is defined by \(Y = 2 X - 3\).
  3. Find the value of each of the following.
OCR MEI Further Statistics A AS 2024 June Q2
9 marks Standard +0.3
2 In a game of chance there are 32 slots, numbered 1 to 32, and on each turn a ball lands in one of them. You may assume that the process is completely random. You are given that \(X\) is the random variable denoting the number of the slot that the ball lands in on a given turn.
  1. Suggest a suitable distribution to model \(X\). You should state the value(s) of any parameter(s).
  2. Write down \(\mathrm { P } ( X = 7 )\). Players of the game start with a score of 0 . On each turn a player may choose to play the game by selecting a number. If the ball lands in the slot with that number then 15 is added to the player's score. Otherwise, the player's score is reduced by 1 . A player's score may become negative. A player decides to play the game, selecting the number 7 on each turn, until the ball lands in the slot numbered 7. You are given that \(Y\) is the random variable denoting the number of turns up to and including the turn in which the ball lands in the slot numbered 7.
  3. Determine \(\mathrm { P } ( Y \leqslant 15 )\).
  4. Determine the player's expected final score.
OCR MEI Further Statistics A AS 2024 June Q3
14 marks Standard +0.3
3 A glassware factory produces a large number of ornaments each week. Just before they leave the factory, all the ornaments are checked and some may be found to be defective. The Quality Assurance Manager of the factory wishes to model the number of defective ornaments that are found each week using a Poisson distribution. The numbers of defective ornaments found each week in a period of 40 weeks are shown in Table 3.1. \begin{table}[h]
\captionsetup{labelformat=empty} \caption{Table 3.1}
No. of defective ornaments in a week, \(r\)0123456\(\geqslant 7\)
No. of weeks with \(r\) defective ornaments, \(f\)2141353120
\end{table} You are given that summary statistics for the data are \(\sum f = 40 , \sum \mathrm { rf } = 84\) and \(\sum \mathrm { r } ^ { 2 } \mathrm { f } = 256\).
  1. By using the summary statistics to determine estimates for the mean and variance of the number of defective ornaments produced by the factory each week, explain how the data support the suggestion that the number of defective ornaments produced each week can be modelled using a Poisson distribution. The Quality Assurance Manager is asked by the head office to carry out a chi-squared hypothesis test for goodness of fit based on a \(\operatorname { Po } ( 2 )\) distribution.
  2. Table 3.2, which is incomplete, gives observed frequency, probability, expected frequency and chi-squared contribution. \begin{table}[h]
    \captionsetup{labelformat=empty} \caption{Table 3.2}
    No. of defective ornaments in a week, \(r\)Observed frequencyProbabilityExpected frequencyChi-squared contribution
    020.135345.41342.15232
    114
    2130.270670.43620
    357.2179
    \(\geqslant 4\)60.142880.01421
    \end{table}
    1. Complete the copy of the table in the Printed Answer Booklet.
    2. Carry out the test at the \(10 \%\) significance level.
  3. On one occasion a fork-lift truck in the factory drops a crate containing eight ornaments and all of them are subsequently found to be defective. Explain why the Poisson model cannot model defects occurring in this manner.
OCR MEI Further Statistics A AS 2024 June Q4
10 marks Standard +0.3
4 A chemist is conducting an experiment in which the concentration of a certain chemical, A , is supposed to be recorded at the start of the experiment and then every 30 seconds after the start. The time after the start is denoted by \(t \mathrm {~s}\) and the concentration by \(\mathrm { z } \mathrm { mg } \mathrm { cm } ^ { - 3 }\). The collected data are shown in the table below. Note that the concentration at \(t = 90\) was not recorded.
Time, \(t\)03060120150
Concentration of A, \(z\)40.031.327.512.811.4
The chemist wishes to plot the data on a graph.
  1. Explain why \(t\) should be plotted on the horizontal axis. You are given that the summary statistics for the data are as follows. \(n = 5 \quad \sum t = 360 \quad \sum z = 123.0 \quad \sum t ^ { 2 } = 41400 \quad \sum z ^ { 2 } = 3629.74 \quad \sum \mathrm { t } = 5835\) The regression line of \(z\) on \(t\) is given by \(\mathbf { z = a + b t }\) and is used to model the concentration of chemical A for \(t \geqslant 0\).
    1. Use the summary statistics to determine the value of \(a\) and the value of \(b\).
    2. Find the value of the residual at each of the following values of \(t\).
      • \(t = 60\)
      • \(t = 120\)
        1. Use the equation of the regression line to estimate the value of the concentration at 90 seconds.
        2. With reference to your answers to part (b)(ii), comment on the reliability of your answer to part (c)(i).
      Further experiments indicate that the model is reasonably reliable for times greater than 150 seconds up to about 200 seconds.
  3. Show that the model cannot be valid beyond a time of about 200 seconds.
OCR MEI Further Statistics A AS 2024 June Q5
10 marks Moderate -0.3
5 A student is investigating possible association between the amount of coffee that an adult drinks each day and the number of hours that they remain awake each day. In an initial investigation, a random sample of 8 adults is selected. The student obtains the following information from each of these adults: the amount of coffee that they drink each day and the number of hours that they remain awake each day. The student analyses the data and finds that the associated product moment correlation coefficient is 0.6030 .
  1. State one assumption that must be made for a hypothesis test based on the product moment correlation coefficient to be carried out. For the remainder of this question you may assume that this assumption is true.
  2. Carry out a test at the \(5 \%\) significance level to investigate whether there is any correlation between amount of coffee drunk and number of hours awake. The student conducts a second investigation which is similar to the first but this time based on a random sample of 30 adults. The product moment correlation coefficient for the new data is 0.5487 . The student carries out an equivalent hypothesis test to the one carried out in part (b), again using a 5\% significance level.
  3. Identify any differences between the two tests and their results. You do not need to restate the hypotheses or explain the conclusion in context.
  4. You may assume the following guidelines for considering effect size.
    Product moment
    correlation coefficient
    		Effect size
    0.1Small
    0.3Medium
    0.5Large
    Explain briefly why the results of the student's second investigation are likely to be more reliable than the results of the initial investigation.
OCR MEI Further Statistics A AS 2024 June Q6
10 marks Moderate -0.8
6 A bank monitors the amounts of cash withdrawn from a cash machine. It categorises any withdrawal of an amount of \(\pounds 50\) or less as 'small' and any withdrawal of an amount greater than \(\pounds 50\) as 'large'. Over a long period of time the bank finds that the proportion of withdrawals that are small is 0.43 .
The bank wishes to model a sample of 10 withdrawals to examine the number of small withdrawals.
    1. State a suitable probability distribution for such a model, justifying your answer.
    2. State one assumption needed for the model to be valid.
    1. Find the probability that exactly 4 of the 10 withdrawals are small.
    2. Find the probability that exactly 4 of the 10 withdrawals are large.
    3. Find the probability that no more than 4 of the 10 withdrawals are large.
  3. Find the probability that, in the 10 withdrawals, the 7th withdrawal is large and there are exactly 3 that are small.
OCR MEI Further Statistics A AS 2020 November Q1
12 marks Moderate -0.3
1 The random variable \(X\) represents the number of cars arriving at a car wash per 10-minute period. From observations over a number of days, an estimate was made of the probability distribution of \(X\). Table 1 shows this estimated probability distribution. \begin{table}[h]
\(r\)01234\(> 4\)
\(\mathrm { P } ( X = r )\)0.300.380.190.080.050
\captionsetup{labelformat=empty} \caption{Table 1}
\end{table}
  1. In this question you must show detailed reasoning. Use Table 1 to calculate estimates of each of the following.
    You should now assume that \(X\) can be modelled by a Poisson distribution with mean equal to the value which you calculated in part (a).
  2. Find each of the following.
OCR MEI Further Statistics A AS 2020 November Q2
12 marks Standard +0.3
2 A researcher is investigating the concentration of bacteria and fungi in the air in buildings. The researcher selects a random sample of 12 buildings and measures the concentrations of bacteria, \(x\), and fungi, \(y\), in the air in each building. Both concentrations are measured in the same standard units. Fig. 2 illustrates the data collected. The researcher wishes to test for a relationship between \(x\) and \(y\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ba3fcd3c-6834-4116-be0e-d5b27aed0a7e-3_595_844_513_255} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure}
  1. Explain why a test based on the product moment correlation coefficient is likely to be appropriate for these data. Summary statistics for the data are as follows. \(n = 12 \quad \sum x = 18030 \quad \sum y = 15550 \quad \sum x ^ { 2 } = 31458700 \quad \sum y ^ { 2 } = 21980500 \quad \sum x y = 25626800\)
  2. In this question you must show detailed reasoning. Calculate the product moment correlation coefficient between \(x\) and \(y\).
  3. Carry out a test at the \(5 \%\) significance level based on the product moment correlation coefficient to investigate whether there is any correlation between concentrations of bacteria and fungi.
  4. Explain why, in order for proper inference to be undertaken, the sample should be chosen randomly.
OCR MEI Further Statistics A AS 2020 November Q3
8 marks Moderate -0.3
3 A child is trying to draw court cards from an ordinary pack of 52 cards (court cards are Kings, Queens and Jacks; there are 12 in a pack). She draws cards, one at a time, with replacement, from the pack. Find the probabilities of the following events.
  1. She draws a court card for the first time on the sixth try.
  2. She draws a court card at least once in the first six tries.
  3. She draws a court card for the second time on the sixth try.
  4. She draws at least two court cards in the first six tries.