Final answer:
The probability of having exactly 4 hurricanes in a year when the expected number is 5.2 is calculated using the Poisson distribution formula. The calculation would use the values 4 for the number of events and 5.2 for the mean, providing the specific probability after computation.
Step-by-step explanation:
The question asks for the probability of a certain number of hurricanes occurring in a year when the expected number (mean) is given. This is a problem in the subject of Mathematics, specifically a part of statistics known as the Poisson distribution. The Poisson distribution is often used to model the number of events happening within a fixed interval of time or space if these events happen with a known constant mean rate and independently of the time since the last event.
To find the probability of there being exactly 4 hurricanes in a year when the average number is 5.2, one would typically use the Poisson probability function: P(x; μ) = (e−μμx) / x!, where 'x' is the number of events, 'μ' is the expected number of events (5.2 in this case), and 'e' is approximately equal to 2.71828.
In this scenario, the calculation would be P(4; 5.2) = (e−5.25.24) / 4!. By inputting the values and performing the calculation, we would find the probability of exactly 4 hurricanes occurring in a year.