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A Level Further Mathematics A
Y542/01 Statistics
OCR A-LEVEL FURTHER MATHEMATICS A
(Y542/01) STATISTICS SUMMER JUNE EXAM
* 9 4 5 9 1 0 3 6 5 7 *
PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. If you need extra space use the lined pages at the end of the Printed
Answer Booklet. The question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be
given for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
–2
• The acceleration due to gravity is denoted by g m s . When a numerical value
is needed use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
1 A researcher wishes to find people who say that they support a specific plan.
Each day the researcher interviews people at random, one after the other,
until they find one person who says that they support this plan. The
researcher does not then interview any more people that day. The total
number of people interviewed on any one day is denoted by R.
(a) Assume that in fact 1% of the population would say that they support the
plan.
(i) State an appropriate distribution with which to model R, giving the
value(s) of any
parameter(s). [1]
(ii) Find P (50 1 R G 150). [2]
The researcher incorrectly believes that the variance of a random variable
2
X with any discrete probability distribution is given by the formula [E (X )] -
E (X).
(b) Show that, for the type of distribution stated in part (a), they will obtain the
correct value of
the variance, regardless of the value(s) of the
parameter(s). [2]
2 The directors of a large company believe that there are more computer failures in
the Head Office when temperatures are higher. They obtain data for the Head
Office for the maximum temperature, T °C, and the number of computer failures, X,
on each of 12 randomly chosen days.
(a) State which of the following words can be applied to T.
Independe
Dependent nt Controlled Response [1]
The data is summarised as
follows.
2 2
n = 12 /t = 261 /x = 41 /t = 5869 /x = 311 /tx = 1021
(b) Calculate the value of the product moment correlation coefficient
r. [2]
(c) The directors wish to investigate their belief using a significance test at
the 1% level.
(i) Explain why a 1-tail test is appropriate in this situation. [1]
(ii) Carry out the test. [6]
(d) One of the directors prefers the temperatures to be given in
Fahrenheit (°F), rather than Centigrade (°C). The relationship
9
between F and C is F = 5 C +32.
, State the value of r that would result from using temperatures in Fahrenheit
in the calculation.
[1]
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