| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2013 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Combined probability with other distributions |
| Difficulty | Standard +0.3 This is a straightforward S1 binomial distribution question requiring students to identify parameters and calculate probabilities using standard formulas. While it involves reading a probability table and applying binomial distribution in context, it requires only routine application of learned techniques with no novel problem-solving or proof elements. |
| Spec | 2.03a Mutually exclusive and independent events2.03b Probability diagrams: tree, Venn, sample space2.03e Model with probability: critiquing assumptions |
### Part (a)(i)
M1: Use of $X \sim B(40, 0.15)$ and calculation of $P(X \leq 10)$
A1: 0.9595 (or 0.960, or 95.95%)
### Part (a)(ii)
M1: Use of $X \sim B(40, 0.50)$ and calculation of $P(X \geq 25)$
A1: 0.0433 (or 0.043, or 4.33%)
### Part (a)(iii)
M1: Use of $X \sim B(40, 0.175)$ and calculation of $P(X = 2)$
A1: 0.0271 (or 0.027, or 2.71%)
### Part (a)(iv)
B1: Identification of appropriate probability = 0.35 (achievement of at least reserve price but not lower estimate)
M1: Use of $X \sim B(40, 0.35)$ and calculation of $P(10 < X < 15)$
M1: Correct calculation of required probabilities
A1: 0.2970 (or 0.297, or 29.70%)
### Part (b)
M1: Calculation of expected value: $E(X) = 40 \times 0.675$ (probability of achieving at least reserve price but not upper estimate)
A1: 27 items
---3 An auction house offers items of jewellery for sale at its public auctions. Each item has a reserve price which is less than the lower price estimate which, in turn, is less than the upper price estimate. The outcome for any item is independent of the outcomes for all other items.
The auction house has found, from past records, the following probabilities for the outcomes of items of jewellery offered for sale.
\hfill \mbox{\textit{AQA S1 2013 Q3 [11]}}