11. Classify each of the following random variables as discrete or continuou a) The time left on a parking meter. b) The number of goals scored by a football player. c) The total pounds of fish caught on a fishing trip. d) The number of cans in a vending machine. e) The time spent by a doctor examining a patient. f) The amount of petrol filled in the car. g) The price of a concert ticket.

Certainly! Here's the classification of each random variable as **discrete** or **continuous**: --- **a) The time left on a parking meter.** - **Type:** **Continuous** - **Explanation:** Time can be measured with infinite precision (e.g., seconds, fractions of a second), allowing for an uncountable number of possible values within a range. --- **b) The number of goals scored by a football player.** - **Type:** **Discrete** - **Explanation:** Goals are counted in whole numbers (0, 1, 2, ...), making the values countable and distinct. --- **c) The total pounds of fish caught on a fishing trip.** - **Type:** **Continuous** - **Explanation:** Weight can be measured with varying degrees of precision (e.g., pounds, ounces), allowing for an infinite number of possible values within a range. --- **d) The number of cans in a vending machine.** - **Type:** **Discrete** - **Explanation:** Cans are counted as whole units (e.g., 10 cans, 25 cans), making the values countable and distinct. --- **e) The time spent by a doctor examining a patient.** - **Type:** **Continuous** - **Explanation:** Time can be measured precisely (e.g., minutes, seconds), allowing for an uncountable number of possible values within a range. --- **f) The amount of petrol filled in the car.** - **Type:** **Continuous** - **Explanation:** Volume can be measured with varying degrees of precision (e.g., gallons, liters), allowing for an infinite number of possible values within a range. --- **g) The price of a concert ticket.** - **Type:** **Continuous** *(Typically treated as continuous in statistical analysis)* - **Explanation:** While prices are often set to the nearest cent, they can be considered continuous for practical purposes because they can take on a vast range of values without meaningful gaps. --- ### Summary Table | **Variable** | **Type** | |------------------------------------------------------|--------------| | a) Time left on a parking meter | Continuous | | b) Number of goals scored by a football player | Discrete | | c) Total pounds of fish caught on a fishing trip | Continuous | | d) Number of cans in a vending machine | Discrete | | e) Time spent by a doctor examining a patient | Continuous | | f) Amount of petrol filled in the car | Continuous | | g) Price of a concert ticket | Continuous | --- Feel free to ask if you need further explanations or examples!