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?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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
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?
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