Final answer:
This question requires understanding the student's context for 'x', which seems related to a statistical scenario involving a Poisson distribution. Without additional context, we cannot choose a correct value for 'x'. However, we can describe how to calculate the Poisson probabilities and expected values.
Step-by-step explanation:
To answer the student's question, we first need to understand that 'x' represents a variable in a statistical context, likely referring to a discrete random variable in a Poisson distribution where X~P(2). This implies that the expected value (λ) is 2. To calculate the probabilities, we use the Poisson probability function:
For P(x = 3), the probability of x being exactly 3 is found using the Poisson formula. Similarly, to find P(1 < x < 4), we need to add up the probabilities for x being 2 and 3. Lastly, P(x ≥ 8) refers to the probability of x being 8 or more, which can be found by subtracting the sum of probabilities from 0 to 7 from 1.
If we assume that the probability of a teenager being reminded to do their chores is a Poisson event, we would use the given data to calculate the expected number of reminders.
When we are talking about an exercise with cards, the variable 'X' could represent the number of times a certain color is drawn.
Choosing the correct value for 'x' in the original question depends on the context, which seems to be missing. Without that context, we cannot definitively select an option among A) 3, B) 5, C) 8, and D) 2. The SEO keywords "expected value", "Poisson distribution", and "probability" are central to understanding this type of question.