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3. California Highway Patrol believe that 65% of the drivers traveling on the 405 freeway are speeding. They plan to set up a radar trap by the Roscoe exit on the 405 and check the speeds of 80 randomly selected cars. a) What is the mean and standard deviation of the sampling distribution for sample proportions? b) Can this distribution be approximated by a normal curve? (Hint: check assumption) c) What is the probability that the proportion of drivers that exceed the speed limit in this sample is less than 60%? d) What is the probability that the proportion of drivers that exceed the speed limit in this sample is between 65% and 75%? e) What sample proportion would be at the 95 percentile of this sampling distribution? 4. The Palmeter Dog Agility Training Camp has a larger than average proportion of clients who compete in the AKC professional events. A confidence interval for the population proportion of dogs that compete in professional events from 100 different training schools is constructed. The lower limit is determined to be 0.08 and the upper limit is determined to be 0.16. Determine the level of confidence that was used to construct the interval