QUESTION No 03 (25 points) The mayor of Rennes city has compiled data on the amount spent by the patients to buying the protective mask and hand sanitizer gel. The data collected indicate that the amount spent of Population (P) 12000 patients follows a normal distribution The data scientist of Rennes city council confirms at 99% confidence level, the confidence interval of the amount spent by the patients in the population (P) is between [ ( 13,4 ; ( 116,6] a) Using the data scientist information, determine the population mean (U) and the population standard division (O). (10 points) The data scientist chose from the population (P) a random sample ($1) of 1000 patients. b) Estimate at 95% confidence level, the mean age of patients in the sample ($1). (5 points) Suppose the mayor chose from the population (P) a random sample ($2) of 610 patients, and he claims, at the 99% confidence level, the amount spent mean in the sample ($2) is between [ E 58,85 ; ( 85, 58]. c) What do you say to this statement? Justify your answer (5 lines max). (10 points)