Men's heights are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches, while women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. (a) What percentage of men must duck when walking through a door that is 72 inches high? (b) What percentage of women must duck when walking through a door that is 70 inches high? (c) What door height would allow at least 95% of men to walk through the door without ducking?

A salon wants to conduct a survey in order to study the consumption pattern of its consumers. The population mean spending on visiting salon per month is unknown with the population standard deviation is assumed to be $200. A random sample of 55 customers is selected and the sample mean spending on visiting salon per month is $800. (a) Construct a 95% confidence interval estimate for the population mean spending by a customer on visiting salon per month. (b) It is suggested to do the second round inspection. This time, the sample size is 120. What is the sampling error at 95% confidence level?