The authors of the paper “Driving Performance While Using a Mobile Phone: A Simulation Study of Greek Professional Drivers” (Transportation Research Part F [2016]: 164–170) describe a study to evaluate the effect of mobile phone use by taxi drivers in Greece. Fifty taxi drivers drove in a driving simulator where they were following a lead car. The drivers were asked to carry out a conversation while driving, and the following distance (the distance between the taxi and the lead car) was recorded. The sample mean following distance was 3.2 meters and the sample standard deviation was 1.11 meters.

a. Construct and interpret a 95% confidence interval for m, the population mean following distance while talking on a mobile phone for the population of taxi drivers.

b. What assumption must be made to generalize this confidence interval to the population of all taxi drivers in Greece?