Problem #1 One Thursday, researchers gave students enrolled in a section of basic Spanish a set of 50 new vocabulary words to memorize. On Friday the students took a vocabulary test. When they returned to class the following Monday they were retested - without advance warning. Both sets of test scores for the 25 students are shown: Fri 42 44 45 48 44 43 41 35 43 48 43 45 47 Mon 36 44 46 38 40 38 37 31 32 37 41 32 44 Fri 50 34 38 43 39 46 37 40 41 48 37 36 Mon 47 34 31 40 41 32 36 31 32 39 31 41 Note: Graph paper is provided on the last page of this assignment to help you with your graphs. You are not required to use it but graphs should be drawn to scale. a) Complete these calculations to check to see if there were any outliers on Monday: Calculate the IQR. . Calculate Q3 + (1.5 x IQR). Any scores greater than this value are outliers. Were there any outliers? Explain. . Calculate Q1 - (1.5 x IQR). . Any scores less than this value are outliers. Were there any outliers? Explain. b) Create side-by-side (i.e. parallel) box plots to compare the distributions of Friday scores and Monday scores. Use a number line drawn to scale when constructing these. c) Describe the distribution of scores on Friday. Use complete sentences. d) Describe the distribution of scores on Monday. Use complete sentences. e) Compare the distribution of scores on Friday and Monday. Use complete sentences; use explicit comparison words and include evidence of your observations.Problem #2 A local restaurant owner surveyed 160 of his customers to determine what type of salad they preferred. He discovered that 63 people preferred ranch dressing over Italian. He also found that 72 customers like both Italian dressing and cheese on their salad. 44 customers prefer no cheese at all. a) Complete the two-way table below summarizing this data. Customer Salad Preferences Cheese No Cheese Total Ranch dressing Italian dressing Total b) For each statement, indicate if it is True or False, and explain your reasoning. Include evidence. Show any calculations. i) The majority of those surveyed preferred Ranch dressing on their salad. ii Over 75% of the customers prefer cheese on their salad. ) Ill) Of those who prefer cheese on their salad, 62% of them prefer Italian dressing. iv) A greater proportion of \"No Cheese\" customers prefer Ranch dressing than do the \"Cheese\" customers. Problem #3 A theater venue sells four different types of tickets. 45% of tickets sold are general admission, 20% are general admission with a meal, 15% are reserved seating, and the remainder are reserved seating with a meal. The venue makes a profit of $6 per general admission ticket, $9 per general admission with a meal, $8 for reserved seating, and $11 for reserved seating with a meal. a) What percent of tickets sold are reserved seating with a meal? b) What is the average profit per ticket for this venue? Problem #4 Here is a histogram showing the weight of bags of pet food from a random sample at the packaging plant. Weight of bags IN; :- 15 Number of bags Weight (In pounds) a) Describe this distribution. b) Do you think this data can be modeled using the Normal distribution? Why or why not? 0) Do you think more or less than 50% of bags were between 49.8 lbs and 50.2 lbs, inclusive? Explain your reasoning. d) Suppose the supervisor picks up the next bag off the packaging line. Would you be surprised if it weighed 49.5 lbs? Explain (CARE)