Since Hubbert proposed the "peak oil" concept to forecast ultimate recovery of crude oil for the U.S. and the world, there have been countless debates over the timing of peak world conventional oil production rate and ultimate recovery. From review of the literature, forecasts were grouped into those that are like Hubbert's with an imminent peak, and those that do not predict an imminent peak. Both groups have bases for their positions. Viewpoints from the two groups are polarized and the rhetoric is pointed and sometimes personal. A big reason for the large divide between the two groups is the failure of both to acknowledge the significant uncertainty in their estimates. Although some authors attempt to quantify uncertainty, most use deterministic methods and present single values, with no ranges. This research proposes that those that do attempt to quantify uncertainty underestimate it significantly. The objective of this thesis is to rigorously quantify the uncertainty in estimates of ultimate world conventional oil production and time to peak rate. Two different methodologies are used. The first is a regression technique based on historical production data using Hubbert's model and the other methodology uses mathematical models. However, I conduct the analysis probabilistically, considering errors in both the data and the model, which results in likelihood probability distributions for world conventional oil production and time to peak rate. In the second method, I use a multiple-experts analysis to combine estimates from the multitude of papers presented in the literature, yielding an overall distribution of estimated world conventional oil production. Giving due consideration to uncertainty, Hubbert-type mathematical modeling results in large uncertainty ranges that encompass both groups of forecasts (imminent peak and no imminent peak). These ranges are consistent with those from the multiple-experts analysis. In short, the industry does not have enough information at this time to say with any reliability what the ultimate world conventional oil production will be. It could peak soon, somewhere in the distant future, or somewhere in between. It would be wise to consider all of these possible outcomes in planning and making decisions regarding capital investment and formulation of energy policy.