Question

A rogue wave is a unusual, unpredictable, large wave that dwarfs those around it. The impact of such a wave can threaten ocean-going vessels, and is thus of interest to various weather forecasting agencies. In the south Atlantic, the average for this rare event is estimated by the European Center for Medium-Range Weather Forecasts to be 0.0377 rogue waves per hour.

What is the probability (correct to 4 decimal places) that a ship will not encounter a rogue wave in a week long south Atlantic voyage?

Show work and type answer please

Answer 1

Probability of rogue wave per hour = 0.0377

Let X be no of waves in a week (=7*24 = 168 hours)

n = 168

mean = = n * p = 168 * 0.0377 = 6.3336

Let x be a random variable which is equal to number of waves in a week ; where X Po (6.336)

We need to find the probabiltiy that there will be no wave in a week i.e. X= 0

P(0) = 0.0018

ANS: Probability that ship will not encounter a rouge wave in a week = 0.0018