**(i)** Answer that shows correct understanding of "independent", in context; not just equivalent to "single" | B1 | Answer that shows correct understanding of "independent", in context; not just equivalent to "single"
| | 2 | Plausible reason, in context, nothing wrong, nothing that suggests "constant average rate"

**(ii)** $0.1730$ | M1 | Correct use of tables or formula, e.g. 3007, or 4405 from Po(5)
| A1 | if Po(7) stated; answer 0.173, 0.1730 or better
| | 2

**(iii)** $Po(35)$ | B1 | $Po(5 \times 7)$ stated or implied
$N(35, 35)$ | M1 | Normal, $\mu = $ their $\lambda$
| A1 | Both parameters correct, allow $35^2$, $\sqrt{35}$
$1 - \Phi\left(\frac{40 - 35}{\sqrt{35}}\right) = 1 - \Phi(0.9297)$ | M1 | Standardise 40 with $\lambda$, $\sqrt{\lambda}$, allow √, cc errors
| A1 | Both $\sqrt{\lambda}$ and cc correct
| A1 | Answer, a.r.t. 0.176 [penalise 0.1765]
| | 6

**(iv)** Must be "values taken by $T$" [or "set $T$"] or clear equivalent | B1 | Must be "values taken by $T$" [or "set $T$"] or clear equivalent
Any hint that they think $T$ is an event gives B0. | | 1 | α "Same chance of occurring anywhere between 1 and 3": 0; β "For values of $T$ between 1 and 3, $T$ is equally likely": 0; γ "Each value of $T$ is equally likely to occur": I