Inspectors have conveniently walked into a shop and chosen 30 packets of Allens Party Mix Lollies. The mean weight of the packets is 181.2 grams with a standard deviation of 3.2 grams. (a) (5 marks) Construct and interpret a 90% confidence interval for the population mean weight of a packet of Allens Party Mix Lollies. (b) (2 marks) What sampling method was used? Was it a good choice? Explain. (c) (2 marks) Is it possible to retain 90% confidence whilst reducing the margin of error in the confidence interval? Explain briefly (you may quote a relevant formula to support your explanation) (d) (3 marks) If the inspectors want to estimate the mean weight of Allens Party Mix Lollies to within +1 gram with 90% confidence and also assuming the standard deviation is 3.2 grams, what is the sample size required? (e) (8 marks) If the true average weight of Allens Party Mix Lollies is 180 grams as stated by the manufacturer on their packets, what is the probability that the mean weight of Allens Party Mix Lollies exceeds 182 grams for a sample of 30 packets with a standard deviation of 3.2 grams?