Answer Happy

SECTION A - STATISTICS IN CIVIL/TRANSPORT ENGINEERING a) When comparing the quality of asphaltic material provided by two plants, X and Y, for a certain highway job, sufficient samples from each plant were taken and tested. The results from Plant X, showed a peaked bell shaped distribution (Lepto-Kurtosis) while those from Plant Y gave a flat shape (Platy- Kurtosis). Which plant, in your opinion, has a better quality control and why? (6 Marks) b) A large highway construction company owns a large fleet of lorries. The company wishes to compare the wearing qualities of two different types of tyres for use on its fleet of lorries. To make the comparison, one tyre of Type A and one of Type B were randomly assigned and mounted on the rear wheels of each of a sample of lorries. Each lorry was then operated for a specified distance and the amount of wear was recorded for each tyre. The results are shown in Table 1. Assuming that tyre Type B is more expensive than tyre Type A, estimate the 95% confidence interval for the difference between the means of the populations of the wear of the tyres and test the hypothesis that there is a significant difference between the two means at the 5% level. Comment on the choice of tyres. (Make any necessary assumptions). Lorry number Table 1 Results from the tyre wear 1 3 10.3 9.7 2 4 5 6 7 Wear of Type A 8.6 9.8 8.8 10.3 11.9 tyres 9.4 11.0 9.1 8.3 10.3 10.8 Wear of Type B 9.8 tyres (20 Marks) c) For a highway bridge, the results of the tensile strengths from a sample of a certain prime coat material at the age of 7 days are as shown in Table 2. Table 2 Results from the sample for the prime coat material Strength 260-290 290-320 320-350 350-380 380-410 410-440 440-470 (kN/m²) Frequency 1 8 35 18 8 1 0 i) Construct a frequency table and clearly show your calculations for the mean tensile strength together with the range and standard deviation representing this sample. (10 Marks) If the permissible tensile strength allowed in design is equal to the mean less 2.33 times the standard deviation indicate whether any of the sampled brittle prime coat test pieces fell below this strength. (4 Marks) iii) What is the probability that in a sample of 12, less than 2 results show a tensile strength below 320 kN/m²? (10 Marks) Total mark for Question 1 is 50