Final answer:
To find the probability that x is 3 or less from a given probability distribution, sum the probabilities for x=0, x=1, x=2, and x=3, resulting in a total probability of 0.88, or 88%.
Step-by-step explanation:
The question asks us to calculate the probability that a random variable x is 3 or less, given its probability distribution. The probability of each outcome for x is given as follows: P(x=0) is 0.12, P(x=1) is 0.2, P(x=2) is 0.2, and P(x=3) is 0.36. To find the probability that x is 3 or less, we must sum the probabilities of x being 0, 1, 2, and 3.
The calculation is simple: add P(x=0), P(x=1), P(x=2), and P(x=3). Therefore, we have:
P(x ≤ 3) = P(x=0) + P(x=1) + P(x=2) + P(x=3) = 0.12 + 0.2 + 0.2 + 0.36 = 0.88
The probability that the random variable x will be 3 or less is 0.88, or 88%. This approach is generally applicable when dealing with a discrete probability distribution and requires the summation of individual outcome probabilities up to the desired value.