1 On average, 1 in 150 components made by a certain machine are faulty. The random variable \(X\) denotes the number of faulty components in a random sample of 500 components.
- Describe fully the distribution of \(X\).
- State a suitable approximating distribution for \(X\), giving a justification for your choice.
- Use your approximating distribution to find the probability that the sample will include at least 3 faulty components.