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Date November 2020 Marks available 2 Reference code 20N.2.AHL.TZ0.H_5
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number H_5 Adapted from N/A

Question

A survey of British holidaymakers found that 15% of those surveyed took a holiday in the Lake District in 2019.

A random sample of 16 British holidaymakers was taken. The number of people in the sample who took a holiday in the Lake District in 2019 can be modelled by a binomial distribution.

State two assumptions made in order for this model to be valid.

[2]
a.i.

Find the probability that at least three people from the sample took a holiday in the Lake District in 2019.

[2]
a.ii.

From a random sample of n holidaymakers, the probability that at least one of them took a holiday in the Lake District in 2019 is greater than 0.999.

Determine the least possible value of n.

[3]
b.

Markscheme

people’s holidays are independent of each other      R1

the proportion is constant (at 0.15)      R1


[2 marks]

a.i.

Χ~B16, 0.15

PΧ3=0.439      (M1)A1


[2 marks]

a.ii.

probability of at least one =1- probability of none

1-0.85n>0.999  OR  0.85n<0.001      (A1)

attempt to solve inequality      (M1)

n42.503

so least possible n=43       A1


[3 marks]

b.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.

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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