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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.

Respuesta :

Answer:

51.323

Step-by-step explanation:

Lower limit = mean - (standard deviation /sample size)* Zr

Upper limit = mean + (standard deviation /sample size)* Zr

Mean = 51.5

Standard deviation = 3.6

Sample size = 40

Zr 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

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