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**stewardt** **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.**

Mr F says: C!!

**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.