3. The Driving Theory Test includes 30 questions which require one answer to be selected from four options.
- Phil ticks answers at random. Find how many of the 30 he should expect to get right.
- If he gets 15 correct, decide whether this is evidence that he has actually done some revision. Use a \(5 \%\) significance level.
Another candidate, Sarah, has revised and has a 0.9 probability of getting each question right.
- Determine the expected number of answers that Sarah will get right.
- Find the probability that Sarah gets more than 25 correct answers out of 30.