Time, Please"Smitty" Smith is a project manager for a large consumer electronics corporation. Although she has been with the company only four years, she has demonstrated an uncanny ability to bring projects in on time, meet technical specifications, and be close to budget.Her latest assignment is a project that will involve merging two existing technologies. She and her team have almost finished developing the proposal that will be presented to a management committee for approval. All that remains to be done is to determine a duration estimate for the project. Smitty wants an estimated duration that will have a $95$ percent probability of being met. The team has constructed a precedence network for the project. It has three paths. The expected durations and standard deviations for the paths are listed below.ExpectedStandard DeviationPathDuration $($weeks$)($weeks$)10$B$142132$QuestionWhat project duration $($in weeks$)$ should Smitty include in the proposal?