| Exam Board | OCR |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Moderate -0.8 This is a straightforward binomial probability calculation requiring only the application of the standard formula P(X=r) for r=0,1,2 and summing, followed by a conceptual comment about sampling with/without replacement. The calculation is routine and the conceptual point about large population size is a standard textbook observation requiring no novel insight. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| "No it doesn't invalidate the calculation" [no reason] | B0 | |
| "Binomial requires not chosen twice" [false] | B0 | |
| "Probability has to be constant but here the probabilities change" | B0 | |
| Same but "probability of being chosen" [false, but allow B1] | B1 | |
| "Needs to be independently chosen but probabilities change" [confusion] | B0 | |
| "Needs to be independent but one choice affects another" [correct] | B2 | |
| "The sample is large so it makes little difference" [false] | B0 | |
| "The population is large so it makes little difference" [true] | B2 | |
| Both correct and wrong reasons (scattergun approach) | B1 |
# Question 2 (Specimen Verbal):
| Answer | Mark | Guidance |
|--------|------|----------|
| "No it doesn't invalidate the calculation" [no reason] | B0 | |
| "Binomial requires not chosen twice" [false] | B0 | |
| "Probability has to be constant but here the probabilities change" | B0 | |
| Same but "probability of being chosen" [false, but allow B1] | B1 | |
| "Needs to be independently chosen but probabilities change" [confusion] | B0 | |
| "Needs to be independent but one choice affects another" [correct] | B2 | |
| "The sample is large so it makes little difference" [false] | B0 | |
| "The population is large so it makes little difference" [true] | B2 | |
| Both correct and wrong reasons (scattergun approach) | B1 | |2 A university has a large number of students, of whom $35 \%$ are studying science subjects. A sample of 10 students is obtained by listing all the students, giving each a serial number and selecting by using random numbers.\\
(i) Find the probability that fewer than 3 of the sample are studying science subjects.\\
(ii) It is required that, in selecting the sample, the same student is not selected twice. Explain whether this requirement invalidates your calculation in part (i).
\hfill \mbox{\textit{OCR S2 2010 Q2 [5]}}