Cambridge International AS & A Level: Mathematics 9709/63
Cambridge International AS & A Level: Mathematics 9709/63
Cambridge International AS & A Level: Mathematics 9709/63
CANDIDATE
NAME
CENTRE CANDIDATE
NUMBER NUMBER
*8199737846*
MATHEMATICS 9709/63
Paper 6 Probability & Statistics 2 May/June 2020
1 hour 15 minutes
INSTRUCTIONS
³ Answer all questions.
³ Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs.
³ Write your name, centre number and candidate number in the boxes at the top of the page.
³ Write your answer to each question in the space provided.
³ Do not use an erasable pen or correction fluid.
³ Do not write on any bar codes.
³ If additional space is needed, you should use the lined page at the end of this booklet; the question
number or numbers must be clearly shown.
³ You should use a calculator where appropriate.
³ You must show all necessary working clearly; no marks will be given for unsupported answers from a
calculator.
³ Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in
degrees, unless a different level of accuracy is specified in the question.
INFORMATION
³ The total mark for this paper is 50.
³ The number of marks for each question or part question is shown in brackets [ ].
JC20 06_9709_63/RP
© UCLES 2020 [Turn over
2
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1 A random sample of 100 values of a variable X is taken. These values are summarised below.
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2 Each day at the gym, Sarah completes three runs. The distances, in metres, that she completes
in the three runs have the independent distributions W ∼ N 1520, 450, X ∼ N 2250, 720 and
Y ∼ N 3860, 1050.
Find the probability that, on a particular day, Y is less than the total of W and X . [5]
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3 The number of customers who visit a particular shop between 9.00 am and 10.00 am has the distribution
Po ,. In the past the value of , was 5.2. Following some new advertising, the manager wishes to test
whether the value of , has increased. He chooses a random sample of 20 days and finds that the total
number of customers who visited the shop between 9.00 am and 10.00 am on those days is 125.
Use an approximating distribution to test at the 2.5% significance level whether the value of , has
increased. [6]
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4 The random variable A has the distribution Po 1.5. A1 and A2 are independent values of A.
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5 Sunita has a six-sided die with faces marked 1, 2, 3, 4, 5, 6. The probability that the die shows a six
on any throw is p. Sunita throws the die 500 times and finds that it shows a six 70 times.
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(b) Sunita believes that the die is fair. Use your answer to part (a) to comment on her belief. [1]
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(c) Sunita uses the result of her 500 throws to calculate an !% confidence interval for p. This interval
has width 0.04.
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6 The length, X centimetres, of worms of a certain type is modelled by the probability density function
T 6
10 − x x − 5 5 ≤ x ≤ 10,
f x = 125
0 otherwise.
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Find the probability that exactly one of them has length less than 6 cm. [5]
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7 A market researcher is investigating the length of time that customers spend at an information desk.
He plans to choose a sample of 50 customers on a particular day.
(a) He considers choosing the first 50 customers who visit the information desk.
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The actual lengths of time, in minutes, that customers spend at the information desk may be assumed
to have mean - and variance 4.8. The researcher knows that in the past the value of - was 6.0. He
wishes to test, at the 2% significance level, whether this is still true. He chooses a random sample of
50 customers and notes how long they each spend at the information desk.
(b) State the probability of making a Type I error and explain what is meant by a Type I error in this
context. [2]
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(c) Given that the mean time spent at the information desk by the 50 customers is 6.8 minutes, carry
out the test. [5]
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(d) Give a reason why it was necessary to use the Central Limit theorem in your answer to part (c).
[1]
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Additional Page
If you use the following lined page to complete the answer(s) to any question(s), the question number(s)
must be clearly shown.
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