| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2024 |
| Session | September |
| Marks | 10 |
| Topic | Binomial Distribution |
| Type | Identify distribution and parameters |
| Difficulty | Moderate -0.8 This is a straightforward binomial distribution identification and application question. Part (i) requires recognizing a standard binomial setup (fixed n, constant p, independent trials) with no conceptual challenge. Parts (ii) and (iii) involve routine calculations using binomial probability formulas—computing P(X=3) and then a nested binomial problem. All steps are textbook-standard with no novel insight required, making this easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.01a Permutations and combinations: evaluate probabilities |
5.
At a factory that makes crockery the quality control department has found that $10 \%$ of plates have minor faults. These are classed as 'seconds'. Plates are stored in batches of 12. The number of seconds in a batch is denoted by $X$.\\
(i) State an appropriate distribution with which to model $X$. Give the value(s) of any parameter(s) and state any assumptions required for the model to be valid.
Assume now that your model is valid.\\
(ii) Find\\
(a) $\mathrm { P } ( X = 3 )$,\\
(iii) A random sample of 4 batches is selected. Find the probability that the number of these batches that contain at least 1 second is fewer than 3 .\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q5 [10]}}