An electricity provider wants to estimate the mean time it takes for customers to get an electrical fault fixed On April 8th 2023 the provider took a random sample of 16 customers who had recently reported an electrical fault and found a mean wait time of 2 hours. Assume the population standard deviation is known to be 0.4 hours. 

Assume that the conditions are satisfied, and do NOT need to be checked. 

a) State the "When" of the data. 

b) Calculate a 90% confidence interval for the mean. 

c) Interpret your confidence interval 

d) Without calculating another confidence interval, explain what would happen to the width of the 90% confidence interval in part b) if we wanted to calculate a 95% confidence interval instead, holding all else the same 

e) Sometimes the electrical fault takes several visits by the repair team, before the fault is fixed. We are further told that the probability the electrical fault is fixed in one visit by the repair team is 0.9. Calculate the probability that the electrical fault is NOT fixed in one visit.