Questions: Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of people in a restaurant that has a capacity of 100. (b) The square footage in square feet of a house. (a) Is the number of people in a restaurant that has a capacity of 100 discrete or continuous? A. The random variable is continuous. The possible values are x=0,1,2, ..., 100 B. The random variable is continuous. The possible values are 0 ≤ x ≤ 100. C. The random variable is discrete. The possible values are 0 ≤ x ≤ 100. D. The random variable is discrete. The possible values are x=0,1,2, ..., 100

Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
(a) The number of people in a restaurant that has a capacity of 100.
(b) The square footage in square feet of a house.
(a) Is the number of people in a restaurant that has a capacity of 100 discrete or continuous?
A. The random variable is continuous. The possible values are x=0,1,2, ..., 100
B. The random variable is continuous. The possible values are 0 ≤ x ≤ 100.
C. The random variable is discrete. The possible values are 0 ≤ x ≤ 100.
D. The random variable is discrete. The possible values are x=0,1,2, ..., 100

Transcript text: Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of people in a restaurant that has a capacity of 100. (b) The square footage in square feet of a house. (a) Is the number of people in a restaurant that has a capacity of 100 discrete or continuous? A. The random variable is continuous. The possible values are $x=0,1,2, \ldots, 100$ B. The random variable is continuous. The possible values are $0 \leq x \leq 100$. C. The random variable is discrete. The possible values are $0 \leq x \leq 100$. D. The random variable is discrete. The possible values are $x=0,1,2, \ldots, 100$

Solution

Solution Steps

Step 1: Determine the Nature of the Random Variable for Part (a)

The random variable in question is the number of people in a restaurant that has a capacity of 100. This variable can only take on integer values, as you cannot have a fraction of a person. Therefore, it is classified as a discrete random variable.

Step 2: State the Possible Values for Part (a)

The possible values for the number of people in the restaurant range from 0 to 100, inclusive. This can be expressed mathematically as: \[ x = 0, 1, 2, \ldots, 100 \]

Step 3: Determine the Nature of the Random Variable for Part (b)

The random variable in question is the square footage of a house. This variable can take on any value within a continuous range, including fractional values. Thus, it is classified as a continuous random variable.

Step 4: State the Possible Values for Part (b)

The possible values for the square footage of a house can be expressed as: \[ 0 \leq x < \infty \]