Step 1: Understanding Taylor's background.
Frederick Winslow Taylor is considered the father of scientific management. He started his career as a worker in 1878 before becoming an engineer and then applying scientific principles to improve industrial efficiency.
Step 2: Analyzing the options.
(A) 1878: Correct. Taylor began his career as a worker in 1878 and later transitioned to an engineer.
(B) 1884: Incorrect. Taylor's engineering career started earlier.
(C) 1901: Incorrect. Taylor became an engineer long before 1901.
(D) 1903: Incorrect. 1903 was a significant year for Taylor, but not the one when he became an engineer.
Step 3: Conclusion.
The correct answer is (A) 1878, as Taylor transitioned from a worker to an engineer in this year.