New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $205 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of $54.

a.What is the probability that a hotel room costs $226 or more per night (to 4 decimals)?

b.What is the probability that a hotel room costs less than $139 per night (to 4 decimals)?

c.What is the probability that a hotel room costs between $199 and $300 per night (to 4 decimals)?

d.What is the cost of the 20% most expensive hotel rooms in New York City? Round up to the next dollar.