| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2012 |
| Session | June |
| Marks | 4 |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Easy -1.8 This is a straightforward normal distribution lookup requiring only standardization (z = (170-160)/6 ≈ 1.67) and reading from tables. It's a single-step routine calculation with no problem-solving element, making it significantly easier than average A-level questions which typically require multiple techniques or conceptual understanding. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
Use of $z = \frac{x - \mu}{\sigma}$ — M1
Use $\sigma = 6$ and $\mu = 160$ — B1
Obtain $z = 1.667$ — A1
Obtain 0.952 — A1 [4]
**Total: [4]**
*Accept 0.9522, 0.9521 but not 0.9515 or 0.9525*3 The lengths of snakes on a tropical island were measured and found to be normally distributed with a mean of 160 cm and a standard deviation of 6 cm . Find the probability that a randomly selected snake has a length of less than 170 cm .
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2012 Q3 [4]}}