1. Based on data from the Bureau of Labor Statisties, the average time taken by an individual to prepare a standard resume is 4.5 hours, and let's assume the distribution is unknown. The standard deviation is assumed to be 1.5 hours. Imagine we randomly sample 50 job seekers. (a) Let XX denote the total time taken by these 50 job seekers to prepare their resumes. What is the distribution of X7 (Show vour calculations and formulas) (b) What is the probability that the total time taken by the 50 job seekers to prepare their resumes is between 220 and 230 hours? (Show your calculations, formulas, and the curve) (c) What is the probability that the total time taken by the 50 job seekers to prepare their resumes is more than 240 hours? (Show your caleulations, formulas, and the curve) (d) Find the 75" percentile for the total time taken by the 50 job seekers to prepare their resumes. (Show your caleulations and formulas) 2. Suppose that a class of professional swimmers is known to swim a distance of 10 kilometers in an average of 150 minutes with a standard deviation of 15 minutes. Consider 36 of the swim sessions. Let X be the average of the 36 swim sessions. () X~ (). (b) Find the probability that the swimmer will average between 147 and 153 minutes in these 36 swim sessions. (Show your calculations, formulas, and the curve) (c) Find the 80th percentile and 25th percentile for the average of these 36 swim sessions. (Show your caleulations, formulas, and the curve) (d) Find the median of the average swimming times. (Show your calculations, formulas, and the curve) 3. The standard deviation of the heights of a certain tree species is known to be approximately 3 feet. If we want to be 90% confident that the sample mean height is within 1 foot of the true population mean height of these trees, how many randomly selected trees must be chosen for the sample? 4. A school district is trying to assess student satisfaction with their cafeteria lunch options. [t is interested in the amount of satisfaction students have with their lunch options. The population standard deviation is unknown. A committee randomly surveyved 61 students. The sample mean was a satisfaction rating of 6 (on a 10-point scale) with a sample standard deviation of 1.5. (a) Which distribution should you use for this problem (Normal or Student's t distribution)? Why? (b) Construct a 95% confidence interval for the population mean satisfaction rating. State the confidence interval and sketch the graph. (c) Interpret the confidence interval. 5. A study in a renowned health journal evaluated a vaccination program. In a test of a random sample of 200 patients who were given the vaceine, 150 showed positive immunity responses. Form a 95 percent confidence interval for the population proportion of such patients that show a positive immunity response after receiving the vaceine. 6. An environmentalist wishes to estimate the proportion of household produets that contain harmful chemicals. (a) If no preliminary study is available, how large a sample size is needed to be 95 percent confident the estimate is within 0.04 of p? (b) In a preliminary study, 140 of 250 household items were found to contain harmful chem- icals. Using this preliminary study, how large a sample size is needed to construct a 95% confidence interval within 0.04 of p