9cc0-f468f5515efa/Practice%20Test%20ONE/test%20ONE/practice%20test%201.pdf 7 7 80% MK Name ID page 7 of 8 17. You wish to buy shirts for a new clothing store. You do not have much space but want to keep your inventory large enough to satisfy most people so you decide to only buy shirts that will fit the majority of people. If neck circumferences are normally distributed with a mean of 15.5 inches and a standard deviation of 2 inches, what is the maximum and minimum neck circumferences that will represent the central 98% of the population? (7 marks) 18. You were hired to analyze the results of the grade 10 literacy tests. There are 12,000 children in your region to be tested. A few weeks later the test your supervisor calls you and asks what the mean score and standard deviation was in your region. You do not have your calculations with you but you do remember that the test results were normally distributed and that your son got a score of 138 and his score was 2.1 standard deviations above the mean. You also recall that the mean was 127. What was the standard deviation for students in your region? (5 marks) 19. Consider the following stem and leaf plot. 26 6 7 7 777899 How many scores are there in the distribution? ( 1 mark) 344567789 4247 What is the Median? (1 mark) 52689 645689 What is the Mode? ( I mark) 70112344578 80012333334 What is the range? (I mark) What ONE or TWO words best describe this distribution? (I mark) acer7 67% + O 13. The following represents data from a student council election at a small school. The total enrolment at the school is 400. number of students who voted 90 -68 868 838 Junior Girls Junior Boys Senior Girls Senior Boys How many boys voted? ( 1 mark) How many girls voted? (I mark) How many seniors voted? (1 mark) How many senior boys voted? (1 mark) What percentage of the entire student body voted? (1 mark) 14. Consider the following sample of scores 31, 34, 32, 32, 38, 35, 30, 31, 32. 34, 35. 35. 40, 37 a ) What is the variance? (4 marks) (mean = 34. EX- = 16.294) b ) What is the standard deviation? (1 mark) W O 15"C A168f5515efa/Practice%20Test%20ONE/test%20ONE/practice%20test%201.pdf 8 2 5 7 80% Computational Questions Please answer all questions in the space provided. If you must use the back of a page CLEARLY indicate which question you are answering. 15. The following table represents the data from 86 amateur marathon runners at a recent event. The numbers are the running time expressed in minutes Class Interval Cum f Cum % rel f 120-124 1 125-129 7 8.14 130-134 8 15 17.44 135-139 13 28 32.56 140-144 15 43 50.00 145-149 12 55 63.96 150-154 12 77.91 155-159 75 87.21 160-164 81 94.19 165-169 86 100 Fill in the missing values. (2 marks) (Note: Only calculate the values that are underlined, DO NOT calculate all the rel f's) b ) You must finish in the top 10% to be eligible for the Boston marathon. How fast do you need to run this race in? (9 marks) the race in 136 minutes how many people finished behind you? (9 marks acerName ID page 6 of 8 16. A psychologist is interested if what people learn through the day can affect how much REM sleep they have at night. A teacher at the St Catharines Music Academy selects 10 students who are learning the Piano. They are all described as exceptional students. During the week before exams when students are practicing very hard to learn new music she measures how much REM sleep each of them has. She compares these results to 10 students randomly selected from the Violin class. They do not have exams for two more weeks so those students are not practicing as hard. She finds that the Piano and Violin groups have an average of 89 and 85 minutes of REM sleep respectively and decides that there is no difference in the amount of REM sleep between groups and concludes that learning and REM sleep are unrelated. Identify the following: a. The population (1 mark) b. The sample(s) (1 mark)_ c. The independent variable(s) (1 mark) d. The dependent variable(s) (1 mark) e. The statistic (1 mark) f. Is this an experiment or observational study? (justify your answer) (1 mark) g. What type of scale is the dependent variable? (justify your answer) (1 mark) h. Identify one major (i.e. obvious) problem with the design of this research and in one or two sentences each describe how you would correct it. (3 marks) NOTE: We have not covered this yet this year so do not concern yourself. acer