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Date	November 2017	Marks available	2	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]

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

[4]

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

$X \sim {\text{Po}}(0.2)$

${\text{P}}(X \geqslant 1) = 1 - {\text{P}}(X = 0)$ (M1)

$= 0.181{\text{ }}( = 1 - {{\text{e}}^{ - 0.2}})$ A1

[2 marks]

EITHER

let $Y$ be the number of bananas eaten in one week

${\text{Y}} \sim {\text{Po}}(1.4)$ (A1)

${\text{P}}(Y = 0) = 0.246596 \ldots {\text{ }}( = {{\text{e}}^{ - 1.4}})$ (A1)

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

$Z \sim {\text{B}}(7,{\text{ }}0.181 \ldots )$ (A1)

${\text{P}}(Z = 0) = 0.246596 \ldots$ (A1)

THEN

$52 \times 0.246596 \ldots$ (M1)

$= 12.8{\text{ }}( = 52{{\text{e}}^{ - 1.4}})$ A1

[4 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » AHL 2.13—Rational functions

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