Question Part Points Submissions Used The number of ships to

Question Part Points Submissions Used The number of ships to arrive at a harbor on any given day is a random variable represented by x. The probability distribution for x is as follows. (Give your answer exactly.) x 19 20 21 22 23 P(x) 0.4 0.2 0.2 0.1 0.1 (a) Find the probability that exactly 22 ships arrive. (b) Find the probability that at least 21 ships arrive. (c) Find the probability that at most 20 ships arrive.

Solution

Let X be the random variable that the number of ships to arrive at a harbor on any given day.

The probability distribution of X is,

(a) Find the probability that exactly 22 ships arrive.

P(exactly 22 ships arrive) = P(X = 22) = 0.1

(b) Find the probability that at least 21 ships arrive.

P(at least 21 ships arrive) = P(X 21) =P(X = 21) + P(X = 22) + P(X = 23)

= 0.2 + 0.1 + 0.1 = 0.4

(c) Find the probability that at most 20 ships arrive.

P(at most 20 ships arrive) = P(X 20) = P(X = 19) + P(X = 20) = 0.4+0.2 = 0.6