Question 2 [(1+2+2)+(2+1) = 8 marks] (a) The following data represents the time (in min) it...

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Question 2 [(1+2+2)+(2+1) = 8 marks] (a) The following data represents the time (in min) it took 6 Western Sydney University students to travel to university on a particular day last semester. 34 22 56 62 19 37 i) Find the median travel time. ii) Find the average travel time. iii) Find the sample standard deviation for the travel time data recorded. (b) Here is monthly rainfall (in mm) recorded at a weather station over a twelve-month period. Values are precise to the nearest whole number. 51 35 68 19 24 13 39 15 26 22 22 17 12 i) Construct a stem and leaf plot of the rainfall data for this twelve-month period. ii) Comment on the symmetry or skewness of the data. Justify your reason for taking this position. Question 3 [3+2 = 5 marks] (a) An engineer is inspecting a batch of rubber washes that have just been fabricated. The engineer has found that the thickness of the washes is normally distributed with a mean thickness of 21.5 mm and a standard deviation of 1.3 mm. If the engineer knows that the thickness of the rubber washes must fall between 25.4 mm and 20.2 mm, find the proportion of washes that will fit the specifications for this product. Please use the Empirical rule to answer this question. (b) If there were 1500 rubber washers in the batch outlined in part (a) above, approximately how many washers would be rejected for being too thin? Question 2 [(1+2+2)+(2+1) = 8 marks] (a) The following data represents the time (in min) it took 6 Western Sydney University students to travel to university on a particular day last semester. 34 22 56 62 19 37 i) Find the median travel time. ii) Find the average travel time. iii) Find the sample standard deviation for the travel time data recorded. (b) Here is monthly rainfall (in mm) recorded at a weather station over a twelve-month period. Values are precise to the nearest whole number. 51 35 68 19 24 13 39 15 26 22 22 17 12 i) Construct a stem and leaf plot of the rainfall data for this twelve-month period. ii) Comment on the symmetry or skewness of the data. Justify your reason for taking this position. Question 3 [3+2 = 5 marks] (a) An engineer is inspecting a batch of rubber washes that have just been fabricated. The engineer has found that the thickness of the washes is normally distributed with a mean thickness of 21.5 mm and a standard deviation of 1.3 mm. If the engineer knows that the thickness of the rubber washes must fall between 25.4 mm and 20.2 mm, find the proportion of washes that will fit the specifications for this product. Please use the Empirical rule to answer this question. (b) If there were 1500 rubber washers in the batch outlined in part (a) above, approximately how many washers would be rejected for being too thin?