Question: a). As product manager of a new brand of toothpaste, assuming you want to achieve 95% reliability, what is the sample size if you want to determine the proportion of households who are aware of your product? Ensure that you are within 4% of the population proportion.

b). Assume that the number of packages processed daily at the local post office in normally distributed. Assume that over 20 days, the standard deviation of the number of packages processed was 39.3. Develop a 99% confidence interval for the population standard deviation.

c). The amount of material used in making a custom sail for a sailboat is normally distributed. For a random sample of 15 sails, you find that the mean amount of material is 912 square feet, with a standard deviation of 64 square feet. Develop a 99% confidence interval for the population mean amount of material used in a custom sail.

d). A researcher is interested in determining the percentage of all households in the U.S. that have more than one home computer. In a survey of 492 households, 27% indicated that they own more than one home computer. Develop a 90% confidence interval for the proportion of all households in the U.S. with more than one computer.

e). In a recent survey of 600 adults, 16.4% indicated that they had fallen asleep in front of the television in the past month. What is the level of confidence associated with the interval of 12.9% to 19.9%?