A petrol station records the amount charged to each customer, rounded to the nearest cent. Which statement best describes this random variable?

1. Discrete, because the charge is rounded and can only take a countable set of values.
2. Discrete, because the amount charged depends on the number of litres purchased.
3. Continuous, because the volume of petrol dispensed can take any value within a range.
4. Continuous, because the amount charged varies between customers.

A random variable \(X\) is defined as the volume of fuel (in litres) dispensed by a bowser per use. Which statement best describes \(X\) ?

1. \(X\) is discrete because the machine dispenses a fixed amount each time.
2. \(X\) is discrete because volume can only take positive values.
3. \(X\) is continuous because the machine is used many times per day.
4. \(X\) is continuous because volume can take any value within an interval.

Which of the following is an example of a continuous random variable?

1. The number of text messages sent by a student in a day
2. The time taken for a swimmer to complete 100 m race
3. The number of cars in a school car park at 9 am
4. The number of siblings a student has

A hospital records the number of patients admitted to the emergency department each day. How would this data best be classified?

1. Discrete, because the number of patients changes every day
2. Discrete, because the count can only take whole number values
3. Continuous, because the number of patients can be very large
4. Continuous, because patient admission is an ongoing process

A scientist measures the wingspan of butterflies in a study. How would this data best be classified?

1. Discrete, because wingspan can be measured precisely
2. Discrete, because each butterfly has a unique wingspan
3. Continuous, because wingspan can take any value within a range
4. Continuous, because there are many butterflies in the study