An airplane has 175 seats. Because some ticketed passengers do not show up, the airline sells 180 seats. The probability that a passenger will not show up is 5 %. Find the probability that exactly 178 passengers will show up and causing a shortage of three seats

The probability that exactly 178 passengers will show up and causing a shortage of three seats is 0.004364

Explanation:

X = number of passengers show up

X follow binomial distribution with n = 180,

p = 1 - 0.05

= 0.95

P (X = 178) = binom. dist (178,180,0.95,0)

= 0.004364

Therefore, The probability that exactly 178 passengers will show up and causing a shortage of three seats is 0.004364