In Exercises 5–8, assume that the Poisson distribution applies...

Question

In Exercises 5–8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 5.5 per year, as in Example 1; and proceed to find the indicated probability.
b. In a 118-year period, how many years are expected to have 10 hurricanes?

b. In a 118-year period, how many years are expected to have 10 hurricanes?

Accepted Answer

Welcome back everyone to another video. With an average of 2 volcanic eruptions per year in a certain area, use the plus on distribution to find the expected number of years with exactly 3 eruptions in a 100 year period. A says 19 years, B 18 years, C 20 years, and D 22 years. So first of all, let's recall that the probability and the plus on distribution where X is equal to K is equal toe to the power of negative lambda, multiplied by lambda raises the power of K divided by K factorial. So we want to define lambda, which is the mean value, and we're given to. And now we're looking at exactly 3 eruptions, which means that K is equal to 3. So the probability of getting 3 eruptions is P X equals 3. And that would be equal to E to the power of negative lambda, so E to the power of -2, multiplied by lambda, which is 2, erase the power of K, so 2 cubed. Divided by K factorial, which is 3 factorial. So now we have our probability, we can definitely calculate it, or we can just immediately evaluate the expected number of years with exactly 3 eruptions. So, our expected value. Is simply the product between the number of years and our probability. So we can say 100 because we're looking at 100 years. Multiplied by the probability value which is he to the power of -2 multiplied by 2 cubed. Divided by 3 factorial, and now we can evaluate the result. When we multiply 100 years by the given probability value, we end up with Approximately 18 years. Which corresponds to the answer to is B. Thank you for watching.