A popular resort hotel has 300 rooms and is usually fully bo

A popular resort hotel has 300 rooms and is usually fully booked. About 6% of the time a reservation is canceled before 6:00 p.m. deadline with no penalty. What is the probability that at least 280 rooms will be occupied? Use binomial distribution to find exact value.

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 280) = Used the excel formula = ROUND(BINOMDIST(280-1,300,0.94,TRUE),3)
= 0.264
P(X>=280) = 1 - P( X < 280) = 1 - 0.264 = 0.736