Jack keef general motors, an automobile dealer in lincoln, nebraska, advertised a $9.99 40-point safety checkup for any car and claimed that the service department would finish the job in less than 30 minutes. a local newspaper reporter selected a random sample of 58 customers who took advantage of the dealer's offer and found the sample mean time to complete the safety checkup was 32.2 minutes. assume that the population standard deviation is 5.7 minutes. a) should a z or t distribution be used for statistical procedures regarding the mean? remember to explain your answer. b) is there any evidence to suggest the true mean time to complete the safety checkup is greater than 30 minutes? perform the hypothesis test at a 1% significance level. include the complete four step hypothesis test including all of the work. c) assume that the appropriate confidence bound is 30.45 minutes, do you think that the true mean time to complete the safety checkup is greater than 30 minutes if the dealership only records the time to the nearest minute? explain your answer. hint: think about the practicality of the situation. d) which confidence bound, upper bound or lower bound, was used in part c)? explain your answer. you will receive 0 points if you do not include an explanation or your explanation includes the results from a calculation