Candidates may use any calculator permitted by Pearson regulations. Calculators
must not have the facility for symbolic algebraic manipulation, differentiation and
integration, or have retrievable mathematical formulae stored in them.
Instructions
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
centre number and candidate number.
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
Answer the questions in the spaces provided
– there may be more space than you need.
You should show sufficient working to make your methods clear. Answers without working may
not gain full credit.
Values from statistical tables should be quoted in full. If a calculator is used instead of tables the
value should be given to an equivalent degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
• The total mark for this part of the examination is 50. There are 6 questions. • Check
– use this as a guide as to how much time to spend on each question.
your
Advice
Read each question carefully before you start to answer it. answer
,s if you have time at the end.
Turn over
,
, 1. Xian rolls a fair die 10 times.
The random variable X represents the number of times the die lands on a six.
(a) Using a suitable distribution for X, find
(i) P(X = 3)
(ii) P(X < 3)
(3)
Xian repeats this experiment each day for 60 days and records the number of days
when X = 3
(b) Find the probability that there were at least 12 days when X = 3
(3)
(c) Find an estimate for the total number of sixes that Xian will roll during these 60 days.
(1)
(d) Use a normal approximation to estimate the probability that Xian rolls a total of
more than 95 sixes during these 60 days.
(4)
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