New York City is the most expensive city in the United States for lodging. The m

Question

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 $53. Use Table 1 in Appendix B.

a. What is the probability that a hotel room costs $227 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 $200 and $301 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.
$ or - Select your answer -moreless

Explanation / Answer

a) P($227 or more)

= P(z > (227 - 204)/53)

= P(z > 0.43)

= 0.1587

b) P(Less than $139)

= P(z < (139 - 204)/53)

= P(z < -1.23)

= 0.1100

c) P($200 < X < $301)

= P((200 - 204)/53 < z < (301 - 204)/53)

= P(-0.08 < z < 1.83)

= 0.4965

d) z score corresponding to top 20% area = 0.84

Hence,

Required cost = 204 + 53*0.84 = $249 or more

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