# Question 1:

## Part (a)

| Answer | Mark | Guidance |
|--------|------|----------|
| Correct set of values for $c$: $\{0, 1, 2, 3, 4, 5, 6, 7, 8\}$ | B1 | Allow $\{\frac{1}{8}, \frac{2}{8}, \ldots, \frac{8}{8}\}$ |
| $P(C = c) = \frac{1}{9}$ for each value | B1ft | Correct probs consistent with discrete uniform distribution; allow as probability function with $P(X=x) = \frac{1}{9}$ for $0 \leq x \leq 8$ provided $x = \{0,1,2,\ldots,8\}$ clearly defined |

## Part (b)

| Answer | Mark | Guidance |
|--------|------|----------|
| $P(C < 4) = \frac{4}{9}$ (accept 0.444 or better) | B1 | For using correct model to get $\frac{4}{9}$ (o.e.) |
| **SC:** If sample space $\{1,\ldots,8\}$ scored B0B1 in (a), allow $P(C<4) = \frac{3}{8}$ to score B1 | | |

## Part (c)

| Answer | Mark | Guidance |
|--------|------|----------|
| Probability lower than expected suggests model is **not** good | B1ft | Comment stating model is or is not good based on their part (a) and probability in (b); $|(b) - 0.315| > 0.05$: allow "not suitable", "not accurate" etc; $|(b) - 0.315| \leq 0.05$: allow comment suggesting it is suitable; **No prob in (b):** allow comparison mentioning 50% or 0.5 rejecting model; **No prob in (b) and no 50% or 0.5 or (b) $> 1$:** scores B0; ignore comments about location or weather patterns |

## Part (d)

| Answer | Mark | Guidance |
|--------|------|----------|
| e.g. Cloud cover will vary from month to month and place to place, so use a non-uniform distribution | B1 | Sensible refinement considering variations in month or location; just saying "not uniform" is B0; **Context & "non-uniform":** allow mention of different locations, months **and** non-uniform, or use more locations to form new distribution with probabilities based on frequencies; **Context & "binomial":** allow mention of different locations, months **and** binomial; **Just refined model:** must be outlined and discrete and non-uniform (e.g. higher probabilities for more cloud cover or lower for less); **Continuous model** e.g. normal is B0 |