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 the 6 p.m. deadline with no penatly. What is the probability that at least 280 rooms will be occupied? Use the binomial distribution to find the 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) = 0.7357