Boat travel is one of the primary options of transport to Volcano Island. Tourists

make reservations with a boat service company to Volcano Island and often cancel

at the last minute or simply fail to show up. A boat can only hold 15 people, and past

records showed that 20% of those who made a reservation did not show up.

Assume that each reservation is for one person and these reservations are made

independently of one another.

Suppose that the boat service decides to book 18 people for each travel.

(i)

Find the probability that on any given boat, at least one tourist holding a

reservation will not have a seat.

(ii)

Find the probability that there will be one or more empty seats for any

randomly selected boat.

(iii)

Determine the mean and standard deviation for the number of tourists who

made reservation and actually showed up.

3/5

(iv)

Suppose a much larger boat that holds 200 tourists is used for a boat travel

to Volcano Island. If the boat service accepts 235 reservations, determine

the probability that at least one tourist will end up without a seat on this boat.