The mayor is interested in finding a 95% confidence interval for the mean number of pounds of trash per person per week that is generated in city. The study included 120 residents whose mean number of pounds of trash generated per person per week was 31.5 pounds and the standard deviation was 7.8 pounds. What is the confidence interval for the mean number of lbs of trash per person per week that is generated in the city?

Answer:A. NormalB. 30.1, 32.9C. 95, 5Step-by-step explanation:A. The sampling distribution follows a normal distributionGiven that the sample size is large, we have that the sample distribution follows a normal distribution according to the central limit theoremB. The 95% confidence interval is given as follows;[tex]CI=\bar{x}\pm z \times \dfrac{s}{\sqrt{n}}[/tex]The number of residents in the study, n = 120 residentsThe sample mean, [tex]\overline x[/tex] = 31.5 poundsThe standard deviation, s = 7.8 poundsThe z-value for 95% confidence level, z = 1.96Therefore, we get;C.I. = 31.5 ± 1.96 × 7.8/√(120)The 95% C.I. ≈ 30.1 ≤ [tex]\overline x[/tex] ≤ 32.9Therefore, we have that with 95% confidence, the population mean number of pounds per person per week is between 30.1 and 32.9C. Therefore, according to the central limit theorem, about 95 percent of the groups of 120 will contain the true population mean number of pounds of trash generated per person per week and about 5 percent will not contain the true population mean number of pounds of trash generated per person per week.