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IB DIPLOMA PROGRAMME
PROGRAMME DU DIPLÔME DU BI
PROGRAMA DEL DIPLOMA DEL BI
M07/5/MATHL/HP3/ENG/TZ2/XX+
MATHEMATICS
HIGHER LEVEL
PAPER 3
Wednesday 16 May 2007 (afternoon)
INSTRUCTIONS TO CANDIDATES
Do not open this examination paper until instructed to do so.
Answer all the questions in one
section only.
Unless otherwise stated in the question, all numerical answers must be given exactly or correct to
three signifcant fgures.
22077209
9 pages
1 hour
© IBO 2007
22077209
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Please start each question on a new page.
Full marks are not necessarily awarded for a correct answer
with no working.
Answers must be supported by working and/or explanations.
In particular, solutions
found from a graphic display calculator should be supported by suitable working, e.g. if graphs are used to
fnd a solution, you should sketch these as part oF your answer.
Where an answer is incorrect, some marks
may be given for a correct method, provided this is shown by written working.
You are therefore advised
to show all working.
SECTION A
Statistics and probability
1.
[Maximum mark:
8]
(a)
The random variable
X
has a geometric distribution with parameter
p
=
1
4
.
What is the value of P(
X
≤
4)?
[3 marks]
(b)
A magazine publisher promotes his magazine by putting a concert ticket at
random in one out of every four magazines.
If you need 8 tickets to take friends
to the concert, what is the probability that you will fnd your last ticket when you
buy the 20th magazine?
[3 marks]
(c)
How are the two distributions in parts (a) and (b) related?
[2 marks]
2.
[Maximum mark:
14]
(a)
In a random sample of 1100 people in Switzerland it was found that 580 of them
had a connection to the Internet.
Calculate the
95 %
confdence interval For the
proportion of people in Switzerland having a connection to the Internet.
[7 marks]
(b)
How large should the sample have been to make the width oF the
95 %
confdence
interval less than
0.02 ?
[7 marks]
M07/5/MATHL/HP3/ENG/TZ2/XX+
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This note was uploaded on 08/15/2011 for the course MATH 141 taught by Professor Diestel during the Fall '08 term at South Carolina.
 Fall '08
 Diestel
 Math, Calculus

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