Question

Ten is the average number of oil tankers arriving each day at a certain port city. The facilities can handle at most 15 tankers per day. What is the probability thaton a given day, tankers will have to be turned away?

Answer 1

A)    Ten is the average number of oil tankers arriving each day at a certain port. The facilities at the port can handle at most 15 tankers per day. What is the probability that on a given day tankers have to be turned away?

Answer 2

3.

Suppose, random variable X denotes number of tankers arriving in the port in a day.

$\tiny X \sim Pois\left ( 10 \right )$

(a)

Probability that on a given day tankers have to be turned away is given by

$\tiny P(X>15)=1-P(X\leq 15)=1-0.9512596=0.0487404$ [Using R-code 'ppois(15,10)']

(b)

Probability that on a given day tankers have to be facilitated is given by

$\tiny P(X\leq15)=0.9512596$    [Using R-code 'ppois(15,10)']

(c)

Probability that on a given day no truck arrived at the port is given by

   [Using R-code 'dpois(0,10)']

P(X = 0) = 0.00004539993

(d)

Probability that on a given day exactly 8 trucks have to be facilitated is given by

$\tiny P(X=8)=0.112599$ [Using R-code 'dpois(8,10)']