True or false: A probability distribution provides a better estimate of project duration than a specific date?

True, good estimation considering all the factors including scheduling, time, budget, quality, resources, critical path, risk and more are the bottom line. 

true. probability distribution take all the elements necessary for project completion while if a specific date is given then work may not be completed till that date due to absence of estimation.

Client side view: In a contract for the delivery of Building/ operational facilities or infrastructure generally the completion date is an agreed specific date. In the event that liquidiated damages are an option then the statement above is false. If the date is not met or extended LDs will may be an owners right. 

Contractor view: the best program is a Critical Path program. The contract generally defines who is responsible for risk and uncertainty, and contractor must take up these entitlements where applicable. Forcasting completion the contractor should consider a senstitivity analysis for each element in order to determine the best and worst outcomes and actively work towards successful project completion. This may include EOT claims, acceleration or acceptance of potential LD's. Each project is different and should be considered on its own merit. In this case the statement is true.

Thanks for invitation, and I am really sorry for my late, because I were  had a lot of work.

Agree with my mentors

In1957, a new managerial planning and control technique was developed, Program Evaluation and Review Technique (PERT) by the U.S. Navy Special Projects Office on the Polaris missile system to support the nuclear submarine projects. It is a technique for estimating and planning a large project. One of its most powerful concepts is the management of probabilities. PERT makes use of simple statistical mathematics in order to come up with a probability distribution for the completion dates of the project milestones, it was designed to provide: (1) Management information on actual and impending problems in completing a project; (2) A continuous status report on active projects for achieving established objectives, completion dates, and the probability of reaching both; and (3) Notation of most and least critical component activities within each project. PERT presented a comprehensive illustration of all major project activities and their interdependencies. In fact, it even provided time requirements needed for completing each component activity. It focused managerial attention on those business activities most vital in meeting the project completion date and identified which resources could be used more effectively if transferred to other phases of a project. Finally, PERT provided a scheme of the project as it occurred, thereby illustrating the effects of managerial changes in the entire project. The ability of PERT to predict future performance and potential future problems through frequency reporting, marked its major departure from previous planning and control techniques which relied heavily on historical data. The estimation of time for the completion of each activity is important in the network analysis; this can be done using three possible assumptions: (1) Most optimistic time (a): This time assumes that everything will go according to minimum amount of difficulties and such situation may occur approximately one percent of time; (2) Most pessimistic time (b): This time assumes that everything will not go according to plan and that the maximum potential difficulties will develop and may occur approximately one percent of time; and (3) Most likely or normal time (m): This is the time that would most often occur, should this effort be reported over again. The estimated time of an activity completion is given by using three estimates that are combined into an expected duration and a standard deviation. The expected completion duration (μ) is assumed to be (1 × a + 4 × m + 1 × b) ÷ 6, and the standard deviation (s) is assumed to be (b–a) ÷6.