Solve the following problems: 1. An insurance company is trying to estimate the average number of sick days that full-time food service workers use per year. A pilot study found the standard deviation to be 2.5 days. How large a sample must be selected if the company wants to be 95% confident of getting an interval that contains the true mean with a maximum error of 1 day? 2. A restaurant owner wishes to find the 99% confidence interval of the true mean cost of a dry martini. How large should the sample be if she wishes to be accurate within P40? A previous study showed that the standard deviation of the price was P45. 3. A health care professional wishes to estimate the birth weights of infants. How large a sample mush she select if she desires to be 90% confident that the true mean is within 6 ounces of the sample mean? The standard deviation of the birth weights is known to be 8 ounces. A. A researcher wishes to estimate the proportion of adult males who are less than 5 feet 5 inches tall. She wants to be 90% confident that her estimate is within 5% of the true proportion. B. If no estimate of the sample proportion is available, how large should the sample size be? 5. Obesity is defined as a body mass index (BMI) of 3 kg/m2 or more. A 95% confidence interval of the percentage of US adults aged 20 years and over who were obese was found to be 22.4% to 23.5%. What was the sample size? 6. How large a sample should be surveyed to estimate the true proportion of college students who do laundry once a week within 3% with 95% confidence?