2013 A-level H2 Mathematics (9740) Paper 2 Question 12 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
The mean number of absences per day is constant.

(ii)

Let A be the number of absentees from Admin Department on n days.

A~\sim~\mathrm{Po}(1.2n)

\mathrm{P}(A=0) = e^{-1.2n} < 0.01

n > 3.8

\therefore, \mathrm{smallest~number~of~days} = 4

(iii)

Let T be the number of absentees from two Departments on 5 days.

T~\sim~\mathrm{Po}(19.5)

\mathrm{P}(T>20) = 1- \mathrm{P}(T \le 20) = 0.397

(iv)

Let S be the number of absentees from two Departments on 60 days.

S~\sim~\mathrm{Po}(234)

Since \lambda = 234 > 10, S ~\sim~N(234, 234) approximately.

\mathrm{P}(200 \le S \le 250) = \mathrm{P}(199.5 \le S \le 250.5) = 0.848

KS Comments:

There are several answers to (i), please refer to school notes. Some students still forget to do continuity correction.

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