State whether each of the following random variables is discrete or continuous.
(a) the number of defective tires on a car
(b) the body temperature of a hospital patient
(c) the number of letters in a word
(d) the number of draws (with replacement) from a deck of cards until a heart is selected
(e) the length of a movie
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(a) The number of defective tires on a car is a discrete random variable. A car can have 0 defective tires, 1 defective tire, 2 defective tires, and so on, but it cannot have a non-integer number of defective tires.
(b) The body temperature of a hospital patient is a continuous random variable. It can take on any value within a certain range (e.g., 96.5 degrees, 97.3 degrees, 98.1 degrees, etc.), not just whole numbers.
(c) The number of letters in a word is a discrete random variable. It can only take on whole number values, such as 1 letter, 2 letters, 3 letters, and so on.
(d) The number of draws (with replacement) from a deck of cards until a heart is selected is a discrete random variable. It can take on whole number values, such as 1 draw, 2 draws, 3 draws, and so on.
(e) The length of a movie is a continuous random variable. It can take on any value within a certain range, such as 90 minutes, 120 minutes, 150 minutes, and so on, not just whole numbers.
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