20N.2.AHL.TZ0.H_2

pestleMathematicsAIHLPaper 220N· ahl-4-17-poisson-distributionsource ↗

Jenna is a keen book reader. The number of books she reads during one week can be modelled by a Poisson distribution with mean $2.6$ .

Determine the expected number of weeks in one year, of $52$ weeks, during which Jenna reads at least four books.

Markscheme / solution

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

let $Χ$ be the random variable “number of books Jenna reads per week.”

then $Χ ~ Po (2.6)$

$P (Χ \geq 4) = 0 .264 (0.263998 \dots)$ (M1)(A1)

$0.263998 \dots \times 52$ (M1)

$= 13.7$ A1

Note: Accept $14$ weeks.

[4 marks]

Examiners’ report

[N/A]