| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795/2 (Pre-U Further Mathematics Paper 2) |
| Year | 2016 |
| Session | Specimen |
| Topic | Approximating the Poisson to the Normal distribution |
| Type | Multiple approximations in one question |
| Difficulty | Standard +0.3 This question involves standard normal approximations to binomial and Poisson distributions with routine continuity corrections. Part (i) requires justifying np>5 and nq>5, then a straightforward z-score calculation. Part (ii) is similarly mechanical: approximate Poisson(36) with Normal(36,36) and find N from tables. While it tests understanding of when approximations are valid, the calculations are textbook applications with no novel problem-solving required. |
| Spec | 2.04d Normal approximation to binomial5.02c Linear coding: effects on mean and variance5.02d Binomial: mean np and variance np(1-p)5.02i Poisson distribution: random events model5.02k Calculate Poisson probabilities5.02m Poisson: mean = variance = lambda |
NOT FOUND
(The mark scheme shown for Question 5 part (i)(a) covers normal approximation to binomial with $np=20$, $npq=16$, but this appears to correspond to a different question number in the paper.)2 (i) The probability that a shopper obtains a parking space on the river embankment on any given Saturday morning is 0.2 . Using a suitable normal approximation, find the probability that, over a period of 100 Saturday mornings, the shopper finds a parking space at least 15 times. Justify the use of the normal approximation in this case.\\
(ii) The number of parking tickets that a traffic warden issues on the river embankment during the course of a week has a Poisson distribution with mean 36 . The probability that the traffic warden issues more than $N$ parking tickets is less than 0.05 . Using a suitable normal approximation, find the least possible value of $N$.
\hfill \mbox{\textit{Pre-U Pre-U 9795/2 2016 Q2}}