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.
Find the expected number of weeks in the year in which Lucca eats no bananas.
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∼Po(0.2)
P(X⩾1)=1−P(X=0) (M1)
=0.181 (=1−e−0.2) A1
[2 marks]
EITHER
let Y be the number of bananas eaten in one week
Y∼Po(1.4) (A1)
P(Y=0)=0.246596… (=e−1.4) (A1)
OR
let Z be the number of days in one week at least one banana is eaten
Z∼B(7, 0.181…) (A1)
P(Z=0)=0.246596… (A1)
THEN
52×0.246596… (M1)
=12.8 (=52e−1.4) A1
[4 marks]