This paper is a continuation of the study in [1]. As shown in [1], a tail probability estimate can differ by as much as 24,000 times due to a distribution choice. The study conducted in [1] developed a methodology that evaluates the distribution choice effects and applied the methodology to the four widely used probability distributions (Normal, Log Normal (LN), Weibull and Gumbel) with the complete failure data (no censoring). This paper extends the study in [1] in the following three aspects: 1). investigating the truncated distribution effects; 2). studying censoring data situations; and 3). extending the estimated probability region from tail end probability of (E-6, E-2) to the entire probability region of (0,1) which covers high probability events such as some warranty data analysis. The results indicate that, in general, a truncated distribution reduces the sensitivity of the distribution choice on the tail end probability estimates. For the censored data, depending on the censoring scheme and percentage of the censoring data points, the distribution choice can be very sensitive and sometimes can provide very misleading tail end probability estimates.