**Text for Educational Website****Hurricane Probability Analysis**For the past 115 years, a certain state suffered 28 direct hits from major (category 3 to 5) hurricanes. Assume this was typical and the number of hits per year follows a Poisson distribution. Complete parts (a) through (d).**(a)** What is the probability that the state will not be hit by any major hurricanes in a single year?- The probability is [ ] (Round to four decimal places as needed.)**(b)** What is the probability that the state will be hit by at least one major hurricane in a single year?- The probability is [ ] (Round to four decimal places as needed.)- Is this unusual? - O Yes - O No**(c)** What is the probability that the state will be hit by at least three major hurricanes in a single year, as happened several years ago?- The probability is [ ] (Round to four decimal places as needed.)- Does this indicate that the hurricane season several years ago in this state was unusual? - O Yes - O No**(d)** What is the probability that the state will be hit by at least two major hurricanes in a single year, as happened last year?- The probability is [ ] (Round to four decimal places as needed.)- Does this indicate that the hurricane season this year in this state was unusual? - O No - O Yes**Instructions**- Fill in the blanks with the calculated probabilities.- Determine the unusualness of the hurricane seasons based on the probabilities.- Use the Poisson distribution formula where necessary to solve the problems.**Note:** There are no graphs or diagrams in the image to explain.

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved.”. Let X be the number of hurricanes in 1 year. The average number of hurricanes experienced in a year is 28/115 = 0.2435 So the distribution of X is X~Pois(0.2435)(a) The required probability of no hurricanes in a year is given by P(X=0) PX=0=e-μ×μxx!=e-0.2453×0.245300!=0.7825(b) The required probability of at least one hurricane in a year is given by P(X>=1) PX≥1=1-PX=0=1-0.7825=0.2175 The obtained probability is significantly large the event of at least one hurricane cannot be considered an unusual event.(c) The required probability of at least three hurricanes in a year is given by P(X>=3) PX≥3=1-PX=0-PX=1-PX=2=1-0.7825-0.1919-0.0235=0.002 The obtained probability is very small which means the event of three hurricanes in a year is an unusual event.