S2 June 2011 Q1
1. A factory produces components. Each component has a unique identity number and it is assumed that 2% of the components are faulty. On a particular day, a quality control manager wishes to take a random sample of 50 components.
The statistic \(F\) represents the number of faulty components in the random sample of size 50.
| Scheme | Marks |
|---|---|
| The list of ID numbers | B1 |
| (1) |
Notes
B1 for idea of list/register/database and identity numbers
NB B0 if referring to the sample or 50 or only part of the population.
| Scheme | Marks |
|---|---|
| \(F \sim \mathrm{B}(50, 0.02)\) | B1 B1 |
| (2) | |
| (3 marks) |
Notes
These must be in part (b) to gain the marks
1st B1 for Binomial distribution
2nd B1 for \(n = 50\) and \(p = 0.02\) or (50,0.02)
NB (0.02, 50) is B0
Po(1) alone is B0B0
For a probability table
1st B1 Use of B(50,0.02) NB \(\mathrm{P}(X = 0) = 0.3642\)
2nd B1 Table must have all 50 values and their probabilities.