# Condé Nast Traveler publishes

Condé Nast Traveler publishes a Gold List of the top hotelsall over the world. The Broadmoor Hotel in Colorado Springscontains 700 rooms and is on the 2004 Gold List. SupposeBroadmoor’s marketing group forecasts a mean demand of 670 roomsfor the coming weekend. Assume that demand for the upcoming weekendis normally distributed with a standard deviation of 30.
a. What is the probability all the hotel rooms will berented?

SOLUTION:

From given data,

Condé NastTraveler publishes a Gold List of the top hotels all over theworld. The Broadmoor Hotel in Colorado Springs contains 700 roomsand is on the 2004 Gold List. Suppose Broadmoor’s marketing groupforecasts a mean demand of 670 rooms for the coming weekend. Assumethat demand for the upcoming weekend is normally distributed with astandard deviation of 30.

The hotel contains 700 rooms

Let X denote the number of rooms on demand

A demand of 670 room is forecast

That is expected number of rooms on demand =670

The demand for the upcoming weekend is normally distributed

with a standard deviation of 30

so X has N ( , )

Z = (X – ) / hasstandard normal distribution

Where

= 670,   = 30

a. What is theprobability all the hotel rooms will be rented

The probability all the hotel rooms will be rented

P(X > 700) =P ( (X – ) / >    (700 -670) / 30)

= P ( Z  > 1 )

= 1 – P ( Z  < 1 )

= 1 – 0.841344746

= 0.158655254

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