​​​ 1. Clearly distinguish in your own words among the features of the three approaches to probability. Under what circumstances would each type be more appropriate than the others? 2. A recent road safety study found that in 77% of all accidents the driver was wearing a seatbelt. Accident reports indicated that 92% of those drivers escaped serious injury (defined as hospitalisation or death), but only 63% of the non-belted drivers were so fortunate. What is the probability that a driver who was seriously injured was not wearing seatbelt? (Use the decision tree method to obtain your answer.) 3. The aptitude test scores of applicants to a university graduate program are normally distributed with mean 500 and standard deviation 60. If the university wishes to set the cut-off score for graduate admission so that only the top 10 percent of applicants qualify for admission, what is the required cut-off score? What percentage of applicants have test scores within two standard deviations of the mean? 4. For the following discuss whether a sample or a census would be preferable. Indicate any assumptions you make: 'An examination of dwellings in a large city to obtain information about the extent of present home insulation and the costs to bring substandard dwellings up to minimum insulation standards.' 5. Comment on the veracity of the following .statements: a) 'The Central Limit Theorem is the cornerstone of statistical estimation.' b) 'The overriding factor in determining sample size is the requirement for precision in estimates of population parameters.' 6. Explain the difference between sampling error and non-sampling error. Briefly describe three types of non-sampling error. 7. How large a sample is needed so that a 95% confidence interval for the mean number of years of attained education has a margin of error equal to one year?