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To test how long coronavirus can stay viable (infectious) on cardboard, 10 sample cardboards were tested for the duration that the virus could be viable on them. The sample mean and standard deviation were found to be 20 and 3.5 hours, respectively. (Disclaimer: This example is made up only for the purpose of assessing your knowledge of statistics and probability and the numbers are not based on actual studies.) a) Based on this test, what is the 99% confidence interval for the mean viability duration of coronavirus on cardboard? (4 marks) What do you practically learn from this finding? (1 marks) b) According to the sample that was collected, coronavirus loses its viability on cardboard after an average of 20 hours. Assuming that the actual standard deviation of the viability duration on cardboard is 2 hours, how many samples must be taken to be 99% confident that the error of estimating this time is less than 1 hour? (3 marks) c) Considering the information about the observed sample, can we be convinced that the actual viability duration has a standard deviation of 2 hours? (4 marks)