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 $55. a. What is the probability that a hotel room costs $225 or more per night (to 4 decimals)? b. What is the probability that a hotel room costs less than $140 per night (to 4 decimals)? c. What is the probability that a hotel room costs between $200 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. $.

A. 0.3515

B. 0.1223

C. 0.4885

D. I cannot figure this one out

Explanation / Answer

for normal distribution z=(X-mean)/.std deviation

a)probability that a hotel room costs $225 or more per night =P(X>225)=1-P(X<225)=1-P(Z<(225-204)/55)

=1-P(Z<0.3818)=1-0.6487=0.3513

b)probability that a hotel room costs less than $140 =P(X<140) =P(Z<-1.1636)=0.1223

c)probability that a hotel room costs between $200 and $300 =P(200<X<300)=P(-0.0727<Z<1.7455)

=0.9595-0.4710=0.4885

d)for 20% most expensive, at 80 percentile z=0.8416

hence corresponding score =mean +z*std deviation =204+0.8416*55=250.29

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