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## How to calculate confidence intervals of normal distributions

a) 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. Suppose the average diameter of a simple random sample of 75 bolts is 5.12 mm. Calculate the margin of error of a 95% confidence interval for the mean then determine the 95% confidence interval.

b) You want to rent an unfurnished one-bedroom apartment in Boston next year. The mean monthly rent for a simple random sample of 30 apartments advertised in the local newspaper is $1,450. The standard deviation of the population is $220. Find a 99% confidence interval for the mean monthly rent for unfurnished one-bedroom apartments available for rent in this community.

c) An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes, handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. One day an inspector randomly checks 50 washers and finds that 5 of them have scratches or dents. Compute a 95% confidence interval for the proportion of appliances from this manufacturer that get damaged during shipment