To find the mean of the probability distribution $X$, we use the formula for the expected value $E(X)$, which is given by:

$E(X) = \sum (X_i \cdot P(X_i))$

Given: $X = \{1, 2, 3\}$ $P(X) = \{0.68, 0.14, 0.89\}$

However, there is an issue here: the probabilities should sum up to 1 in a valid probability distribution. Let's check the sum of the given probabilities:

$0.68 + 0.14 + 0.89 = 1.71$

Since the sum of the probabilities is greater than 1, this is not a valid probability distribution. Therefore, the mean cannot be determined from this information.

So, the correct answer is:

$d) \text{Cannot be determined.}$

Would you like more details or have any questions? Here are some questions you might want to ask:

1. How do you find the mean of a valid probability distribution?
2. What are the properties of a probability distribution?
3. How do you handle invalid probability distributions?
4. Can you explain expected value in more detail?
5. What are some examples of valid probability distributions?

Tip: When working with probability distributions, always ensure that the sum of the probabilities equals 1 to confirm it is valid.