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Date November 2017 Marks available 4 Reference code 17N.2.AHL.TZ0.H_6
Level Additional Higher Level Paper Paper 2 Time zone Time zone 0
Command term Find Question number H_6 Adapted from N/A

Question

The number of bananas that Lucca eats during any particular day follows a Poisson distribution with mean 0.2.

Find the probability that Lucca eats at least one banana in a particular day.

[2]
a.

Find the expected number of weeks in the year in which Lucca eats no bananas.

[4]
b.

Markscheme

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

let X be the number of bananas eaten in one day

XPo(0.2)

P(X1)=1P(X=0)     (M1)

=0.181 (=1e0.2)     A1

[2 marks]

a.

EITHER

let Y be the number of bananas eaten in one week

YPo(1.4)     (A1)

P(Y=0)=0.246596 (=e1.4)     (A1)

OR

let Z be the number of days in one week at least one banana is eaten

ZB(7, 0.181)     (A1)

P(Z=0)=0.246596     (A1)

THEN

52×0.246596     (M1)

=12.8 (=52e1.4)     A1

[4 marks]

b.

Examiners report

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

Syllabus sections

Topic 2—Functions » AHL 2.13—Rational functions
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Topic 2—Functions

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