Statistics
posted by Richa
A popular resort hotel has 300 rooms and is usually fully booked. About 4% of the time a reservation is cancelled before 6:00 PM deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find the exact value and the normal approximation to the binomial and compare your answers.

MathMate
Using Binomial probability function, we are looking for:
P(280≤X≤300)
=Σ C(300,r)p^r*(1p)^(300r)
for r=280, 281, ...300, and
C(300,r)=300!/((300r)!r!)
=0.00896+0.01530+0.02474+0.03777+0.05427+...+0.00004+0.0000
=0.98992
Using normal approximation with continuity correction, we have
n=300, p=0.96,μ=np=288,σ=sqrt(npq)=3.3941
P(280≤X≤300)
=1Φ(279.5,288,3.3941)
=0.99386
Error = (0.993860.98992)/0.98992=0.4%.
If we look at the tail, the performance is much worse. The reason for the poor performance (if we look at the tail) is because
np=300*0.96=288 >> 10
npq=300*0.96*0.04= 11.52 ~ 10.
If we use Camp Paulson approximation, we get
1P(279≤X≤300)
=0.98982 (error=0.0096%, much better)
Ref:
http://www.johndcook.com/blog/camp_paulson/
Respond to this Question
Similar Questions

math  statistics
Rooms NO of units 1 471 2 1470 3 11715 4 23468 5 24476 6 21327 7 13782 8+ 15647 compute the following conditional probablilites directly that is, do not use the conditional probability rule. For a U.S. housing unit selected at random, … 
Finite Math
Please help...i'm totally lost with this one. Construct a linear program for the following situation. Do not solve. A hotel is refurbishing its rooms, each type of which will accommodate either one or two persons. A oneperson room … 
statistics
Consider the average available for all hotel rooms from the previous assignment. Identify the point estimate of the average number of available hotel rooms in this lesson from each sample. Construct and Interpret a 95% confidence level … 
BUSSINESS STATISTICS
Consider the average available for all hotel rooms from the previous assignment. Identify the point estimate of the average number of available hotel rooms in this lesson from each sample. Construct and Interpret a 95% confidence level … 
PreCalculus
The Hotel Bellville has 400 rooms. Currently the hotel is filled . The daily rental is $ 250 per room. For every $ 14 increase in rent the demand for rooms decreases by 5 rooms. Let x = the number of $ 14 increases that can be made. … 
math
Help pleaseeee The Hotel Regal has 500 rooms. Currently the hotel is filled. The daily rental is $ 400 per room. For every $4 increase in rent the demand for rooms decreases by 8 rooms. Let x be the number of rooms that are being rented … 
Math
The Hotel Regal has 600 rooms. Currently the hotel is filled . The daily rental is $ 250 per room. For every $ 4 increase in rent the demand for rooms decreases by 4 rooms. Let x = the number of $ 4 increases that can be made. What … 
precalculus
The Hotel Florence has 550 rooms. Currently the hotel is filled . The daily rental is $ 700 per room. For every $ 14 increase in rent the demand for rooms decreases by 7 rooms. Let x = the number of $ 14 increases that can be made. … 
precalculus
The Hotel Thomasina has 500 rooms. Currently the hotel is filled . The daily rental is $ 1000 per room. For every $ 4 increase in rent the demand for rooms decreases by 8 rooms. Let x = the number of $ 4 increases that can be made. … 
C++
Write a program that prompts the user to enter the cost of renting one room,the number of rooms booked,the number of days the rooms are booked and the sales tax (as a percent). I am confused on how to start