Questions — OCR Further Statistics AS (58 questions)

Browse by module
All questions AEA AS Paper 1 AS Paper 2 AS Pure C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Extra Pure Further Mechanics Further Mechanics A AS Further Mechanics AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics Further Paper 4 Further Pure Core Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Pure with Technology Further Statistics Further Statistics A AS Further Statistics AS Further Statistics B AS Further Statistics Major Further Statistics Minor Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 H240/01 H240/02 H240/03 M1 M2 M3 M4 M5 Mechanics 1 P1 P2 P3 P4 PMT Mocks PURE Paper 1 Paper 2 Paper 3 Pure 1 S1 S2 S3 S4 SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics Stats 1 Unit 1 Unit 2 Unit 3 Unit 4
Browse by board
AQA AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further AS Paper 1 Further AS Paper 2 Discrete Further AS Paper 2 Mechanics Further AS Paper 2 Statistics Further Paper 1 Further Paper 2 Further Paper 3 Discrete Further Paper 3 Mechanics Further Paper 3 Statistics M1 M2 M3 Paper 1 Paper 2 Paper 3 S1 S2 S3 CAIE FP1 FP2 Further Paper 1 Further Paper 2 Further Paper 3 Further Paper 4 M1 M2 P1 P2 P3 S1 S2 Edexcel AEA AS Paper 1 AS Paper 2 C1 C12 C2 C3 C34 C4 CP AS CP1 CP2 D1 D2 F1 F2 F3 FD1 FD1 AS FD2 FD2 AS FM1 FM1 AS FM2 FM2 AS FP1 FP1 AS FP2 FP2 AS FP3 FS1 FS1 AS FS2 FS2 AS M1 M2 M3 M4 M5 P1 P2 P3 P4 PMT Mocks Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 OCR AS Pure C1 C2 C3 C4 D1 D2 FD1 AS FM1 AS FP1 FP1 AS FP2 FP3 FS1 AS Further Additional Pure Further Additional Pure AS Further Discrete Further Discrete AS Further Mechanics Further Mechanics AS Further Pure Core 1 Further Pure Core 2 Further Pure Core AS Further Statistics Further Statistics AS H240/01 H240/02 H240/03 M1 M2 M3 M4 Mechanics 1 PURE Pure 1 S1 S2 S3 S4 Stats 1 OCR MEI AS Paper 1 AS Paper 2 C1 C2 C3 C4 D1 D2 FP1 FP2 FP3 Further Extra Pure Further Mechanics A AS Further Mechanics B AS Further Mechanics Major Further Mechanics Minor Further Numerical Methods Further Pure Core Further Pure Core AS Further Pure with Technology Further Statistics A AS Further Statistics B AS Further Statistics Major Further Statistics Minor M1 M2 M3 M4 Paper 1 Paper 2 Paper 3 S1 S2 S3 S4 SPS SPS ASFM SPS ASFM Mechanics SPS ASFM Pure SPS ASFM Statistics SPS FM SPS FM Mechanics SPS FM Pure SPS FM Statistics SPS SM SPS SM Mechanics SPS SM Pure SPS SM Statistics WJEC Further Unit 1 Further Unit 2 Further Unit 3 Further Unit 4 Further Unit 5 Further Unit 6 Unit 1 Unit 2 Unit 3 Unit 4
OCR Further Statistics AS Specimen Q2
2 The probability distribution of a discrete random variable \(W\) is given in the table.
\(w\)0123
\(\mathrm { P } ( W = w )\)0.190.18\(x\)\(y\)
Given that \(\mathrm { E } ( W ) = 1.61\), find the value of \(\operatorname { Var } ( 3 W + 2 )\).
OCR Further Statistics AS Specimen Q3
3 Carl believes that the proportions of men and women who own black cars are different. He obtained a random sample of people who each owned exactly one car. The results are summarised in the table below.
\cline { 2 - 3 } \multicolumn{1}{c|}{}BlackNon-black
Men6971
Women3055
Test at the 5\% significance level whether Carl's belief is justified.
OCR Further Statistics AS Specimen Q4
4
  1. Four men and four women stand in a random order in a straight line. Determine the probability that no one is standing next to a person of the same gender.
  2. \(x\) men, including Mr Adam, and \(x\) women, including Mrs Adam, are arranged at random in a straight line. Show that the probability that Mr Adam is standing next to Mrs Adam is \(\frac { 1 } { X }\).
OCR Further Statistics AS Specimen Q7
7 The discrete random variable \(X\) is equally likely to take values 0,1 and 2 .
\(3 N\) observations of \(X\) are obtained, and the observed frequencies corresponding to \(X = 0 , X = 1\) and \(X = 2\) are given in the following table.
\(x\)012
Observed
frequency
\(N - 1\)\(N - 1\)\(N + 2\)
The test statistic for a chi-squared goodness of fit test for the data is 0.3 . Find the value of \(N\).
OCR Further Statistics AS Specimen Q8
8 The following table gives the mean per capita consumption of mozzarella cheese per annum, \(x\) pounds, and the number of civil engineering doctorates awarded, \(y\), in the United States in each of 10 years.
\(x\)9.39.79.79.79.910.210.511.010.610.6
\(y\)480501540552547622655701712708
  1. Find the equation of the regression line of \(y\) on \(x\). You are given that the product moment correlation coefficient is 0.959 .
  2. Explain whether this value would be different if \(x\) is measured in kilograms instead of pounds. It is desired to carry out a hypothesis test to investigate whether there is correlation between these two variables.
  3. Assume that the data is a random sample of all years.
    (a) Carry out the test at the \(10 \%\) significance level.
    (b) Explain whether your conclusion suggests that manufacturers of mozzarella cheese could increase consumption by sponsoring doctoral candidates in civil engineering. {www.ocr.org.uk}) after the live examination series. If OCR has unwittingly failed to correctly acknowledge or clear any third-party content in this assessment material, OCR will be happy to correct its mistake at the earliest possible opportunity. For queries or further information please contact the Copyright Team, First Floor, 9 Hills Road, Cambridge CB2 1GE.
    OCR is part of the Cambridge Assessment Group; Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge. }
OCR Further Statistics AS 2024 June Q4
  1. Find the probability that 4 telephone calls are received in a randomly chosen one-minute period.
  2. A sample of 10 independent observations of \(X\) is obtained. Find the expected number of these 10 observations that are in the interval \(2 < X < 8\). It is also known that
    \(P ( X + Y = 4 ) = \frac { 27 } { 8 } P ( X = 2 ) \times P ( Y = 2 )\).
  3. Determine the possible values of \(\mathrm { E } ( Y )\).
  4. Explain where in your solution to part (c) you have used the assumption that telephone calls and e-mails are received independently of one another.
OCR Further Statistics AS Specimen Q5
  1. The random variable \(X\) has the distribution \(\operatorname { Geo } ( 0.6 )\).
    (a) Find \(\mathrm { P } ( X \geq 8 )\).
    (b) Find the value of \(\mathrm { E } ( X )\).
    (c) Find the value of \(\operatorname { Var } ( X )\).
  2. The random variable \(Y\) has the distribution \(\operatorname { Geo } ( p )\). It is given that \(\mathrm { P } ( Y < 4 ) = 0.986\) correct to 3 significant figures. Use an algebraic method to find the value of \(p\). Sabrina counts the number of cars passing her house during randomly chosen one minute intervals. Two assumptions are needed for the number of cars passing her house in a fixed time interval to be well modelled by a Poisson distribution.
  3. State these two assumptions.
  4. For each assumption in part (i) give a reason why it might not be a reasonable assumption for this context. Assume now that the number of cars that pass Sabrina's house in one minute can be well modelled by the distribution \(\operatorname { Po } ( 0.8 )\).
  5. (a) Write down an expression for the probability that, in a given one minute period, exactly \(r\) cars pass Sabrina's house.
    (b) Hence find the probability that, in a given one minute period, exactly 2 cars pass Sabrina's house.
  6. Find the probability that, in a given 30 minute period, at least 28 cars pass Sabrina's house.
  7. The number of bicycles that pass Sabrina's house in a 5 minute period is a random variable with the distribution \(\operatorname { Po } ( 1.5 )\). Find the probability that, in a given 10 minute period, the total number of cars and bicycles that pass Sabrina's house is between 12 and 15 inclusive. State a necessary condition.
OCR Further Statistics AS 2018 June Q6
6 In this question you must show detailed reasoning. The random variable \(T\) has a binomial distribution. It is known that \(\mathrm { E } ( T ) = 5.625\) and the standard deviation of \(T\) is 1.875 . Find the values of the parameters of the distribution.