A sample of 45 washing machines are collected in order to give an indication of the average approximate weight of a washing machine. The average weight from this sample is found to be 75.5 kg. The population mean weight of these machines is unknown, but the population standard deviation is thought to be 4.4 kg.

a) Create a 95% confidence interval for the mean weight of all washing machines. SHOW YOUR WORKINGS, and give your answers correct to two decimal places.

b) Interpret your confidence interval.

c)Without calculating another confidence interval, and holding all else constant, would a 99% confidence interval be narrower, wider or the same width as the 95% confidence interval you created in part a)? Briefly explain.