| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2025 |
| Session | January |
| Marks | 9 |
| Topic | Binomial Distribution |
| Type | Verify conditions in context |
| Difficulty | Moderate -0.8 This is a straightforward binomial distribution question requiring only standard knowledge: stating conditions for binomial model (routine recall), using cumulative binomial tables, and computing P(X≥7) and P(X=7). All parts are textbook exercises with no problem-solving insight required, making it easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)5.02c Linear coding: effects on mean and variance |
2. On average, $25 \%$ of the packets of a certain kind of soup contain a voucher. Kim buys one packet of soup each week for 12 weeks. The number of vouchers she obtains is denoted by $X$.\\
(i) State two conditions needed for $X$ to be modelled by the distribution $\mathrm { B } ( 12,0.25 )$.
In the rest of this question you should assume that these conditions are satisfied.\\
(ii) Find $\mathrm { P } ( X \leqslant 6 )$.
In order to claim a free gift, 7 vouchers are needed.\\
(iii) Find the probability that Kim will be able to claim a free gift at some time during the 12 weeks.\\
(iv) Find the probability that Kim will be able to claim a free gift in the 12th week but not before.\\[0pt]
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\hfill \mbox{\textit{SPS SPS SM Statistics 2025 Q2 [9]}}