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Date November 2020 Marks available 3 Reference code 20N.2.AHL.TZ0.H_9
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number H_9 Adapted from N/A

Question

The weights, in grams, of individual packets of coffee can be modelled by a normal distribution, with mean 102g and standard deviation 8g.

Find the probability that a randomly selected packet has a weight less than 100g.

[2]
a.

The probability that a randomly selected packet has a weight greater than w grams is 0.444. Find the value of w.

[2]
b.

A packet is randomly selected. Given that the packet has a weight greater than 105g, find the probability that it has a weight greater than 110g.

[3]
c.

From a random sample of 500 packets, determine the number of packets that would be expected to have a weight lying within 1.5 standard deviations of the mean.

[3]
d.

Packets are delivered to supermarkets in batches of 80. Determine the probability that at least 20 packets from a randomly selected batch have a weight less than 95g.

[4]
e.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

Χ~N102, 82

PΧ<100=0.401        (M1)A1


[2 marks]

a.

PΧ>w=0.444       (M1)

w=103 g        A1


[2 marks]

b.

PΧ>100Χ>105=PΧ>100Χ>105PΧ>105       (M1)

=PΧ>100PΧ>105        (A1)

=0.158650.35383

=0.448       A1


[3 marks]

c.

EITHER


P90<Χ<114=0.866        (A1)


OR


P-1.5<Z<1.5=0.866        (A1)


THEN


0.866×500       (M1)

=433         A1


[3 marks]

d.

p=PΧ<95=0.19078         (A1)

recognising  Y~B80, p        (M1)

now using  Y~B80, 0.19078        (M1)

PY20=0.116          A1


[4 marks]

e.

Examiners report

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e.

Syllabus sections

Topic 4—Statistics and probability » AHL 4.17—Poisson distribution
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Topic 4—Statistics and probability

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