3. (Total 30 points) A research firm conducted a survey to determine the mean amount of cash steady smokers spend on cigarettes during a week. (a) (15 points) Determine 87% confidence interval for the mean amount of cash spent on cigarettes if sample of 49 steady smokers was found to have spent a mean amount of $20. The population standard deviation for the cash spent is given to be $5. (b) (15 points) Determine 99% confidence interval for the mean amount of cash spent on cigarettes if a sample of 12 smokers was found to have spent a mean amount of $18 with a variance of $36