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 $54. Using EXCEL.

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 $143 per night (to 4 decimals)?

c. What is the probability that a hotel room costs between $201 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 -more or less

Answer 1

Solution-A:

X~N(204,54)

P(X>225)

LEFT TAIL PROB IN EXCEL

=NORMDIST(225,204,54,TRUE)

=0.651321

1-left tail =right tail prob

right tail=1-0.651321

=0.348679

=0.3487

0.3487

b. What is the probability that a hotel room costs less than $143 per night (to 4 decimals)

P(X<143)

=NORMDIST(143,204,54,TRUE)

=0.129316

=0.1293

0.1293

c. What is the probability that a hotel room costs between $201 and $301 per night (to 4 decimals)

P(201<X<301)

P(X<301)-P(X<201)

==NORMDIST(301,204,54,TRUE)-=NORMDIST(201,204,54,TRUE)

=0.963776297-0.477847936
=
0.485928361

0.4859

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

Fro 20% zscore in excel

=NORM.S.INV(0.2)

-0.84162=x-204/54

x=-0.84162*54+204

x= 158.5525

x=159

ANSWER:159