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 time it takes for a light bulb to burn out. (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 (b) Is the time it takes for a light bulb to burn out discrete or continuous? A. The random variable is discrete. The possible values are t=1,2,3, ... B. The random variable is continuous. The possible values are t=1,2,3, ... C. The random variable is discrete. The possible values are t>0. D. The random variable is continuous. The possible values are t>0.

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 time it takes for a light bulb to burn out. (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 (b) Is the time it takes for a light bulb to burn out discrete or continuous? A. The random variable is discrete. The possible values are t=1,2,3, ... B. The random variable is continuous. The possible values are t=1,2,3, ... C. The random variable is discrete. The possible values are t>0. D. The random variable is continuous. The possible values are t>0.
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 time it takes for a light bulb to burn out. (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 $x=0,1,2, \ldots, 100$ (b) Is the time it takes for a light bulb to burn out discrete or continuous? A. The random variable is discrete. The possible values are $t=1,2,3, \ldots$. B. The random variable is continuous. The possible values are $t=1,2,3, \ldots$ C. The random variable is discrete. The possible values are $t>0$. D. The random variable is continuous. The possible values are $t>0$.
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Solution

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Solution Steps

Step 1: Determine if the random variable is discrete or continuous

Since the variable of interest, the number of people in a restaurant, is the number of people in a restaurant with a given capacity of 100, it is inherently countable. Therefore, the random variable is ^discrete^.

Step 2: State the possible values of the random variable

The possible values that the number of people in a restaurant can take are whole numbers ranging from 0 up to the capacity of the restaurant, inclusive.

Final Answer:

Step 1: Determine if the random variable is discrete or continuous

Since the variable of interest, the time it takes for a light bulb to burn out, pertains to a physical measurement that can vary continuously, such as amount of snowfall, distance a baseball travels, or weight of a steak, the random variable is ^continuous^.

Step 2: State the possible values of the random variable

The possible values that the time it takes for a light bulb to burn out can take depend on the context but generally include all real numbers within a specified range. For instance, if we consider weight or distance, the range could be all non-negative real numbers.

Final Answer:

The random variable the time it takes for a light bulb to burn out is continuous, typically taking values in a range such as all non-negative real numbers.

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