Question

Condé Nast Traveler publishes a Gold List of the top hotels all over the world. The Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List. Suppose Broadmoor’s marketing group forecasts a mean demand of 670 rooms for the coming weekend. Assume that demand for the upcoming weekend is normally distributed with a standard deviation of 30.

a. What is the probability all the hotel rooms will be rented?

Answer 1

SOLUTION:

From given data,

Condé Nast Traveler publishes a Gold List of the top hotels all over the world. The Broadmoor Hotel in Colorado Springs contains 700 rooms and is on the 2004 Gold List. Suppose Broadmoor’s marketing group forecasts a mean demand of 670 rooms for the coming weekend. Assume that demand for the upcoming weekend is normally distributed with a standard 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 - ) / has standard normal distribution

Where

= 670 ,   = 30

a. What is the probability 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