| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/3 (Pre-U Mathematics Paper 3) |
| Year | 2016 |
| Session | Specimen |
| Marks | 5 |
| Topic | Normal Distribution |
| Type | Multiple probability calculations only |
| Difficulty | Moderate -0.8 This is a straightforward application of normal distribution with clearly stated parameters. Both parts require only standardizing values and reading from tables (or using a calculator), with no conceptual challenges or multi-step reasoning—simpler than the average A-level question which typically involves more problem-solving. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
**Question 1**
(i) $z = \frac{27 - 24}{4} = 0.75$
$P(X > 27) = P(Z > 0.75)$ [M1]
$= 0.2266$ [A1]
(ii) $P(X \leqslant 25) - P(X \leqslant 20) = P(Z \leqslant 0.25) - P(Z \leqslant -1)$ [M1]
$0.5987 - (1 - 0.8413)$ [M1]
$= 0.44$ [A1]
**Total: 5 marks**1 The times for a motorist to travel from home to work are normally distributed with a mean of 24 minutes and a standard deviation of 4 minutes. Find the probability that a particular trip from home to work takes\\
(i) more than 27 minutes,\\
(ii) between 20 and 25 minutes.
\hfill \mbox{\textit{Pre-U Pre-U 9794/3 2016 Q1 [5]}}