Confidence Interval for when is known

When we know the population standard deviation, we can estimate the true population mean with a sample by using

1. The standard normal distribution and Confidence Level 1- to findz/2
2. Using the samplemeanx, population standard deviation, and Margin of Error FormulaE = z/2 n
3. Give the confidence interval byx-E < < x + E.

A hardware manufacturer produces bolts used to assemble various machines. Assume that the diameter of bolts produced by this manufacturer has an unknown population mean and the standard deviation, is 0.1 mm. A simple random sample of 50 bolts is taken and has average 5.11 mm. Construct a 98% confidence interval for .

You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a simple random sample of 32 apartments advertised in the local newspaper is $ 1, 400. Assume that the standard deviation is known to be $ 220. Find a 99% confidence interval for the mean monthly rent for unfurnished one-bedroom available for rent in this community.