Question

Because of bad weather, the number of days next week that the captain of a charter fishing boat can leave port is uncertain. The following probability distribution for the number of days that the boat is able to leave port per week was determined based on historical data when the weather was poor: The number of days the boat can leave port per week Probability 0 0.20 1 0.05 2 0.05 3 0.05 4 0.15 5 0.10 6 0.15 7 0.25 Based on the probability distribution, what is the expected number of days per week the captain can leave port. Group of answer choices 3.55 4.00 3.50 4.05 2.85

Answer 1

The expected number of days per week the captain can leave port is 4.05.

Explanation:

We are given the following distribution:

`P(X = 0) = 0.2`

`P(X = 1) = 0.05`

`P(X = 2) = 0.05`

`P(X = 3) = 0.05`

`P(X = 4) = 0.15`

`P(X = 5) = 0.1`

`P(X = 6) = 0.15`

`P(X = 7) = 0.25`

What is the expected number of days per week the captain can leave port.

We multiply each outcome by its probability. So

`E = 0*0.2 + 1*0.05 + 2*0.05 + 3*0.05 + 4*0.15 + 5*0.1 + 6*0.15 + 7*0.25 = 4.05`

The expected number of days per week the captain can leave port is 4.05.