A random sample of 30 observations was made on the time taken for people to do a particular task (in minutes). The sample mean was found to be 3.96 and the sample variance was found to be 1.88.

(a) (5 marks) Construct a 95% confidence interval for the expected value (mu) of the time taken.

(b) (2 marks) Interpret the confidence interval.

(c) (3 marks) State any assumptions that you needed to make in order for your answers to part (a) to be valid.