New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $55.

a. What is the probability that a hotel room costs $225 or more per night?

b. What is the probability that a hotel room costs less than $140 per night?

c. What is the probability that a hotel room costs between $200 and $300 per night?

d. What is the cost of the 20% most expensive hotel rooms in New York City?