(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.

(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]