New York City is the most expensive city in the United State

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.

What is the probability that a hotel room costs between $200 and $300 per night (to 4 decimal places)

Solution

P(200<X<300) = P((200-204)/55<Z<(300-204)/55) = P(-0.07<Z<1.74) = 0.9591 - (1-0.5279) = 0.4870