Answer:
B. The variable is continuous because it is not countable.
Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.
Step-by-step explanation:
Previous concepts
A discrete random variable "has a countable number of possible values" in a domain defined. So then the possible values for these types of random variables are the integers.
A continuous is a random variable "where the data can take infinitely many values" that means that can take values from the rational with decimals. Ans is not countable.
Solution to the problem
Let's analyze one by one the possible options:
A. The variable is discrete because it is countable.
False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 1200.56 mi and we can't express this as a discrete random variable.
B. The variable is continuous because it is not countable.
Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.
C. The variable is discrete because it is not countable.
False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 504.67 Km and we can't express this as a discrete random variable.
D. The variable is continuous because it is countable.
False the variable is continuous but cannot be countable since that's the opposite from the definition of continuous random variable.
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