1. The quality control manager at a lightbulb factory needs to estimate the mean life of a new type of lightbulb. The population standard deviation is assumed to be 100 hours. A random sample of 60 lightbulbs shows a sample mean life of 350 hours. Construct and explain a 95% confidence interval estimate of the population mean life of the new lightbulb.
2. A stationary store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 25 greeting cards indicates a mean value of $1.67 and the sample standard deviation is $0.32. Assuming a normal distribution, construct and explain a 95% confidence interval estimate of the mean value of all greeting cards in the store's inventory.
3. A telephone company wants to estimate the porportion of households that would purchase an additional service line if it were made available at a substantially reduced cost. A random sample of 500 households is selected and the results indicate that 135 of the households would purchase the additional service. Construct and explain a 99% confidence interval estimate of the proportion of all households that would purchase the additional service.