Question 2 (12 marks) Marks a. According to the Australian Taxation Office, 25% of small business employment tax returns contained errors that resulted in a tax penalty to the owner. The histogram below obtained from RStudio shows the tax penalties for a sample of 40 small business owners New South Wales: Histogram of Tax Penalties i. Frequency 0 2 4 6 8 10 TTTT 200 400 600 800 1000 1200 1400 Tax Penalties (in $) Describe the shape of the distribution of tax penalties for improperly filed employment tax returns. [1] ii. From the histogram, will the median tax penalty be larger or smaller than the mean? [1] Question 2 (continued) b. The boxplot below represents the marks (in %) obtained by a sample of students in their Intra-session Exam1 in Statistics for Academic Purposes. i. 40 63 74.5 82 96 + + 40 50 55 60 70 75 80 95 % Mark obtained What percentage of students received a mark of at most 82%? ii. Calculate the range. III. Calculate the inter-quartile range. Page 5 of 35 Marks [1] [1] [1] c. There is an evident increase in the number of IT support request at a certain college during the previous term. The recorded number of calls and emails received by the IT Support team per week during the previous term are shown below. 54 62 70 41 35 40 38 55 62 30 48 56 72 Question 2 (continued) Marks d. The distribution of time spent on the job is approximately bell shaped and according to a Human Resources report, a worker in the industrial countries spends on average 420 minutes a day on the job. Suppose the standard deviation of time spent on the job is 35 minutes. i. What will Gary's z score be suppose he spent 450 minutes on the job? [1] ii. III. According to the Empirical Rule, 95% of the data values lies between what two values above and below the mean? [1] According to the Empirical Rule, what percentage of the data values lie between 385 minutes and 490 minutes? Question 2 (continued) [1] Page 7 of 35 Marks e. In the final examination in Introductory Chemistry, the mean grade of a group of students was 65 and the standard deviation was 7. In Mathematics for Health Science, however, the mean final grade of the group was 73 and the standard deviation was 9. i. Calculate the coefficient of variation for Introductory Chemistry and Mathematics for Health Science final exam score. In which subject was there a lesser relative dispersion? [2]