| Date | May 2015 | Marks available | 3 | Reference code | 15M.2.hl.TZ2.4 |
| Level | HL only | Paper | 2 | Time zone | TZ2 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
Emma acquires a new cell phone for her birthday and receives texts from her friends. It is assumed that the daily number of texts Emma receives follows a Poisson distribution with mean \(m = 5\).
(i) Find the probability that on a certain day Emma receives more than \(7\) texts.
(ii) Determine the expected number of days in a week on which Emma receives more than \(7\) texts.
Find the probability that Emma receives fewer than \(30\) texts during a week.
Markscheme
(i) \(X \sim Po(5)\)
\({\text{P}}(X \ge 8) = 0.133\) (M1)A1
(ii) \(7 \times 0.133 \ldots \) M1
\( \approx 0.934{\text{ days}}\) A1
Note: Accept “\(1\) day”.
[4 marks]
\(7 \times 5 = 35\;\;\;\left( {Y \sim Po(35)} \right)\) (A1)
\({\text{P}}(Y \le 29) = 0.177\) (M1)A1
[3 marks]
Total [7 marks]
