4. (18 points / 3 points each) Mileages for taxi rides from Penn Station to their destination are approximately normally distributed with a mean of µ = 4.3 miles and a standard deviation of σ = 1.2 miles.
a. Classify this problem by type using the letter choices:
A. binomial probability problem, C. normal probability problem about a single X,
B. uniform probability problem, D. normal probability problem about a
E. none of the above.
b. What is the probability that a taxi ride is greater than 6 miles?
c. What is the probability that a taxi ride is between 1 and 3 miles?
d. What is the expected length of any given taxi ride?
e. Find the taxi ride mileage that would represent the 80th percentile or P80.
e. If the longest 15% of taxi rides receive a discount, determine the mileage for which customers would receive the discount.