A sanitation department is interested in estimating the mean amount of garbage per bin for all bins in the city. In a random sample of 40 bins, the sample mean amount was 51.5 pounds and the sample standard deviation was 3.6 pounds. Construct 95% and 99% confidence intervals for the mean amount of garbage per bin for all bins in the city.What is the lower limit of the 95% interval? Give your answer to three decimal places.

Answer:51.323Step-by-step explanation:Lower limit = mean - (standard deviation /sample size)* Zr Upper limit = mean + (standard deviation /sample size)* Zr Mean = 51.5Standard deviation = 3.6Sample size = 40Zr depends on confidence interval Zr for 95% = 1.96 Zr for 99% = 2.58 For 95% Lower limit = 51.5 - (3.6 /40)* 1.96 = 51.323 Upper limit = 51.5 + (3.6 /40)* 1.96 = 51.676 For 99% Lower limit = 51.5 - (3.6 /40)* 2.58 = 51.267 Upper limit = 51.5 + (3.6 /40)* 2.58 = 51.732