Unit: BSC100 Build SAMPLE BSC1( X ] SECTION B Example Assessing Daf Give exam + / Fit to page Page view A') Read QUESTION 1 [15 marks] Part marks shown in [ ] One model for predicting the time taken to complete a running race based on information about previous races, is the Riegel model which was first proposed in 1977. The equation is T2 = T, (D2/ D.)1 0 where T: and Dj are the time and distance previously run; D2 is the distance to be run and the prediction for the time taken on this new run is Tz. Distance and time must be measured in consistent units, To investigate the effectiveness of the Riegel model, data was collected for some runners over different distances. The model prediction time was calculated for a 200m race distance and the actual run time was then recorded for each runner. Runner Reigel model Actual 200m run prediction (secs) time (secs) A 26.2 28.1 B 27 20 29.3 31.01 24.2 40.86 37.6 29.40 29.8 27 94 31 8 a) Plot an appropriate bar graph of the data which would help in this investigation. Label your graph clearly [5] O Fi 2 LSAMPLE BSC1( X | SECTION Bearpl | | 0 asse + Fit to page Pa BSC100: Building Blocks for Science Students SAMPLE EXAMINATION PAPER b) Comment on the effectiveness of this model in predicting race times, based on this data set. Make reference to your graph. [3] c) Use the Reigel model to calculate the expected time for Bill to run a race of distance 100m based on Bill's previous performance of running 400m in 82 seconds. [2] d) An athletics coach records the performance times (in seconds) for his athlete to run 400m at each weekly training session for 3 months. He plots the results in a scatterplot ( x = number of weeks of training, y = performance time) and uses Excel to fit two mathematical models to the data. The results are Model 1 : y = -2.25x + 88.61 with R' = 0.710 Model 2 : y = 88.7 932 with R: = 0.034 Which model seems better at explaining the change in the athlete's performance times over the weeks of training? Explain your reasoning [21 According to Model 1, did the athlete's performance times improve? Use this model to estimate the change in the athlete's performance times from weeks 1 to 4. 131 L