2023 MI P2 Q7

The probability that a student is present in school on a typical day is \(0.96\). In a particular school, there are \(28\) students in each class. The number of students in a class who are present in school on a typical school day is denoted by the random variable \(X\). A student is considered absent if he is not present in school the whole day. Assume that \(X\) can be modelled by a binomial distribution.

1. Find the probability that all students in a class are present in school on a typical school day.[1]
2. Find the most likely number of students who are present in school on a typical school day.[1]

An investigation by the form teacher will be carried out if there are more than \(2\) students in the class who are not present in school on a typical school day.

3. Find the probability that an investigation is carried out on a typical school day.[2]

There are \(16\) classes in a level. The school leaders must be alerted if an investigation has to be carried out in at least a third of the classes in the level.

4. Find the probability that the school leaders are alerted on a typical school day.[3]