After receiving his doctoral degree, Turnbull was a visiting faculty member at Stanford University with joint appointments in the Department of Statistics
and the School of Medicine. In 1972 he was appointed lecturer at the Mathematical Institute, University of Oxford, and concurrently a fellow of Jesus College,
Oxford. He joined the Cornell faculty in 1976. In 1979 he was awarded the Snedecor Memorial Award by the American Statistical Association in recognition
of his research. He has been a consultant to many organizations, including the Oak Ridge National Laboratory. Turnbull has served on the Board of Directors
of the National Institute of Statistical Sciences, and on the Expert Review Panel for the National Toxicology Program Board of Scientific Counselors. He is on
the Data and Safety Monitoring Committees for several major national and international clinical trials for the prevention of cancer and of AIDS sponsored by
the National Institutes of Health. He has been on the editorial board of two statistical journals and is currently an associate editor of Statistics in Medicine.
He is a Fellow of the American Statistical Association and of the Royal Statistical Society. He is also a member of the Institute for Operations Research and
the Management Sciences, the Biometric Society, and the Institute of Mathematical Statistics.