MTH 225 Exam 1 Name:- DIRECTIONS: SHOW ALL WORK!! A final response following a calculation should be a sentence. Place a box around your final response. Round probability calculations to 4 decimal places. Round other numerical results including percents to two decimal places (e.g. 2.56 shoes, 18.49%). 1. The public works division selects a random sample of 250 households and measures the volume of water consumption for each household over the course of a week. In addition to the weekly consumption, the household's service zone and the number of individuals listed as residents will be recorded. (a) Identify an individual, the population, the sample, and all variables measured in this study. Classify each variable as qualitative (Q), discrete (D), or continuous (C): individual population sample variable(s) (b) Is this investigation a designed experiment or an observational study? Justify. 2. Identify the sampling method for each scenario. (a) A TSA officer selects the first 19 travelers coming through security for an enhanced inspection. (b) A warehouse management company randomly selects 40 of the 400 properties it manages and inspects every loading dock for any potential repairs. (c) The commanding officer of the 34th Infantry Division will randomly select 40 soldiers from each of its 20 battalions to complete a survey regarding the workplace environment. 3. Below is a histogram for the years of service by the faculty members at State U. (a) Describe the shape of the distribution. (b) Do you expect the mean number of years to be less than, greater than, or about the same as the median? Explain.4. A prospective borrower's debt-to-income ratio is the percent of his/her monthly income that is already committed to personal debt. Below are data for 12 recent applicants. D/I (6) 33.23 34.15 30.35 32.13 49.17 19.95 41.42 29.78 54.63 25.55 36.38 37.43 (a) Sketch a modified boxplot of the data. Are there any potential outliers? If so, which value(s)? (b) What is the IQR for debt-to-income ratios? (c) What is the z-score for the applicant who had a debt-to-income ratio of 29.78%? Interpret this result. 5. A machine used in the production of a frozen pizza is designed to cut balls of dough according to a bell-shaped curve with a mean of 10 ounces and a standard deviation of 0.15 ounces. (a) What percent of dough balls weigh less than 9.70 ounces? (b) What percent of dough balls weigh between 9.55 oz and 10.30 oz? (c) What is the cutoff for the heaviest 0.15% at dough balls