Question

Can you please show work in Excel terms?

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $203 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 $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 $200 and $299 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 -morelessItem 5

Answer 1

X :- Hotel room rate per night

Part a)  What is the probability that a hotel room costs $225 or more per night

P ( X > 225 ) = 1 - P ( X < 225)

Standardizing the value

P ( X > 225 ) = 1 - P ( X < 225)

P ( X > 225 ) = 1 - P ( Z < - 277 )

P ( X > 225 ) = 1 - 0.0028

P ( X > 225 ) = 0.9972

In Excel =1-NORMSDIST( Z value ( -2.77) )

Part b) P ( X < 143 )

P ( Z < - 1.13 ) = 0.1288

In Excel NORMSDIST( Z value ( - 1.13) )

Part c) P ( 200 < X < 299 )

P ( 200 < X < 299 ) = P ( -0.06 < Z < 1.18 )

P ( 200 < X < 299 ) = P ( Z < 1.18) - P ( Z < - 0.06 )

P ( 200 < X < 299 ) = 0.9650 - 0.4774

P ( 200 < X < 299 ) = 0.4875

In Excel NORMSDIST( Z = 1.81) - NORMSDIST(Z = -0.06)

Part d)

P ( Z > ? ) = 20%

P ( Z < ? ) 1 - 205 = 1 - 0.2 = 0.8

Z = 0.84 looking for the probability 0.8 in standard Normal table to calculate critical value Z

X = 248