What is the smallest possible value for x when
1 answer:
You might be interested in
Answer:
(a) The probability that all the hotel's rooms will be rented is 0.1587.
(b) The probability that 50 or more rooms will not be rented is 0.2514.
Step-by-step explanation:
We are given that 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.
Let X = <u><em>demand for rooms in the hotel</em></u>
So, X ~ Normal()
The z-score probability distribution for the normal distribution is given by;
Z = ~ N(0,1)
where, = mean demand for the rooms = 670
= standard deviation = 30
(a) The probability that all the hotel's rooms will be rented means that the demand is at least 700 = P(X 700)
P(X 700) = P(
) = P(Z
1) = 1 - P(Z < 1)
= 1 - 0.8413 = <u>0.1587</u>
The above probability is calculated by looking at the value of x = 1 in the z table which has an area of 0.8413.
(b) The probability that 50 or more rooms will not be rented is given by = P(X 650)
P(X 650) = P(
) = P(Z
-0.67) = 1 - P(Z < 0.67)
= 1 - 0.7486 = <u>0.2514</u>
The above probability is calculated by looking at the value of x = 0.67 in the z table which has an area of 0.7486.