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2024 Oxford Cambridge and RSA A Level Further Mathematics B (MEI) Y422/01 Statistics Major ACTUAL QUESTION PAPER WITH MERGED MARKING SCHEME $7.39
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OXFORD CAMBRDGE
AND RSA 2024
[Type the document subtitle]
OCR 2024
2024
[Type the company address]
, Oxford Cambridge and RSA
Friday 14 June 2024 – Afternoon A
Level Further Mathematics B (MEI) Y422/01
Statistics Major
Time allowed: 2 hours 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(MEI)
• a scientific or graphical calculator
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 page 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 your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 120.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
,OCR is an exempt Charity
Turn over
, 2
Section A (27 marks)
1 The number of insurance policy sales made per month by a salesperson is modelled by the
random variable X, with probability distribution shown in the table.
(a) Find each of the following.
• E(X )
• Var(X ) [2]
The salesperson is paid a basic salary of £1000 per month plus £500 for each policy that is sold.
(b) Find the mean and standard deviation of the salesperson’s monthly salary. [3]
2 The number of cars arriving per minute to queue at a drive-through fast-food restaurant is
modelled by the random variable X. The standard deviation of X is 0.6. You should assume
that arrivals are random and independent and occur at a constant average rate.
(a) Find the mean of X. [2]
(b) (i) Calculate P(X = 1). [1]
(ii) Calculate P(X 2 1). [2]
(c) Find the probability that fewer than 5 cars arrive in a randomly chosen 20-minute period. [2]
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