Approximately once a month cars are shipped from Rotterdam, Holland to Lagos, Nigeria. The past data collection indicates that the weight of a car is normally distributed with the mean of 1,070 kg and the standard deviation 310 kg. The merchant ship that transports the cars has a hundred dedicated "parking spaces" and a maximum load of 114 metric tons (114 thousand kg).
a. What is the probability that the combined weight of 100 randomly selected cars will exceed the maximum weight? How is this performed in R?
b. If the weight of the car is not normally distributed (for example, about half of the vehicles are small passenger cars and the rest are large SUVs), what is the approximate distribution of the mean weight of the sample of 100 vehicles? Which result are you using to justify this answer?