Question 1Helpful notes and hints: Recall that calculating the sample mean and sample standard deviation in Excel were covered in Learning Module 2: Descriptive Statistics (scroll down to ‘Learning Activities’). You can ﬁnd videos on how to create Excel tables and ﬁgures under Learning Module 3: Data Visualization (scroll down to ‘Learning Activities’). The empirical rule was discussed in Learning Module 8: Continuous random variables and continuous probability distributions part 2.(a) Create a boxplot (a box-and-whisker display) of the continuous variable ‘Product weight’, and provide the ﬁve-number summary. Ensure your boxplot has an appropriate vertical axis title and an overall title, and include the units. [8 marks](b) What is the shape of the distribution? Answer in one sentence. [1 mark](c) Are there any extreme values? Answer yes or no, and identify any extreme values that exist according to your boxplot. [1 mark](d) Where is the centre of the distribution? Answer using the appropriate measure of centrality for a box-and-whisker display, and say which measure of centrality you are reporting. [1 mark](e) What is the spread of the distribution? Answer using an appropriate measure of variability for a box-and-whisker display (i.e. report the IQR or the range, and say which one you are reporting). [1 mark](f) Calculate and interpret 68%, 95%, and 99.7% tolerance intervals for the product height. Round each bound to the nearest whole number. Make sure to include the units. [6 marks] 3(g) Suppose the engineers on your design team have indicated that each unit of product should be between 50 and 95 mm tall. Are 95% of units of manufactured product likely to meet the engineering design speciﬁcations? Answer yes or no and explain why or why not in a single sentence. [1 mark](h) How many of the units in your sample do you expect to lie within the 68% tolerance interval? The 95% tolerance interval? The 99.7% tolerance interval? Round each value to the nearest whole number. Show your work. [3 marks]Question 2 Helpful notes and hints: Sample proportions were discussed in the context of contingency tables in Learning Module 3. You will also need material on the binomial and the Poisson distributions from Learning Module 6. To help you with showing your work in Word, please see the video posted under Evaluations (Assignments, Quizzes and Exams) > Case Analysis Project > Showing your work in Question 2.(a) Create a contingency table. The row variable should be product colour, and the column variable should be product shape. If you create the table in Excel, copy/paste it into your word processor. Ensure your contingency table has appropriate labels. Include the row and column totals, and the grand total. [6 marks](b) What is the sample proportion of units that are both red and rectangular? Show your work using proper notation. Provide your answer to 2 decimal places. [2 marks](c) What is the sample proportion of units that are triangular, given that they are yellow? Show your work using proper notation. Provide your answer rounded to 4 decimal places. [2 marks](d) Notice that a product is either rectangular or triangular. What is the probability that, in a random sample of 10 units, there are more than 8 rectangular units of product? Show your work using proper notation. Round your answer to 4 decimal places. Assume that the population proportion of rectangular products is the same as the sample proportion of rectangular products (Hint: you can ﬁnd this sample proportion using your contingency table in part (a)). [4 marks](e) Suppose 2 units of product is manufactured each 10 minutes, on average. Suppose also that there is some variability in the process that can speed it up, or slow it down. What is the probability that between 8 and 12 units of product, inclusive, are manufactured in the next hour? Show your work using proper notation. Round each calculated probability to four decimal places. Note: the word ‘inclusive’ means ‘including 8, 12, and all values in between’. [4 marks]all requirements in attachment
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