Question

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 $54.

a. What is the probability that a hotel room costs $224 or more per night (to 4 decimals)?

b. What is the probability that a hotel room costs less than $141 per night (to 4 decimals)?

c. What is the probability that a hotel room costs between $199 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 -moreless

Answer 1

The distribution given here is:

a) The probability here is computed as:

Converting it to a standard normal variable, we get:

Getting the above probability from the standard normal tables, we get:

Therefore 0.3487 is the required probability here.

b) The required probability here is P(X < 141 )

Converting this to a standard normal variable, we get:

Getting this from the standard normal tables, we get:

Therefore 0.1255 is the required probability here.

c) The required probability here is:

P( 199 < X < 299 )

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.4918 is the required probability here.

d) From the standard normal tables, we have:

P(Z > 0.8416) = 0.2

Therefore the cost here is computed as:

X = Mean + Std Dev*0.8416 = 203 + 54*0.8416 = $248.4464