Question

Suppose the number X of tornadoes observed in kansas during a 1-year period has a poisson distribution with lambda = 9. Compute the following probabilities. Number of tornadoes observed is less than equal to 5

Number of tornadoes observed is between 6 and 9 (inclusive).

Answer 1

To compute the probability that the number of tornadoes observed is less than or equal to 5, we use the poissoncdf(9, 5) formula. The probability that the number of tornadoes observed is between 6 and 9 (inclusive) is found by subtracting the CDFs for X = 5 and X = 9 using the poissoncdf formula.

Step-by-step explanation:

To compute the probability that the number of tornadoes observed is less than or equal to 5, we need to calculate the cumulative distribution function (CDF) for X = 5. Using the formula poissoncdf(9, 5), we find that P(X ≤ 5) = 0.1036.

Similarly, to compute the probability that the number of tornadoes observed is between 6 and 9 (inclusive), we subtract the CDFs for X = 5 and X = 9. Using the formula poissoncdf(9, 5) - poissoncdf(9, 9), we find that P(6 ≤ X ≤ 9) ≈ 0.6137.

Answer 2

Calculating probabilities with the Poisson distribution involves summing individual probabilities for exact numbers or using cumulative functions for ranges. With a mean of 9, P(X ≤ 5) and P(6 ≤ X ≤ 9) are calculated using the poissoncdf function.

Step-by-step explanation:

The student's question pertains to calculating probabilities using the Poisson distribution, specifically with a mean (λ) of 9. To find the probability of the number of tornadoes observed being less than or equal to 5, we need to calculate P(X ≤ 5). We do this by calculating the sum of probabilities from X = 0 to X = 5 using the poissoncdf function.

For the range where the number of tornadoes observed is between 6 and 9, inclusive, we need to calculate P(6 ≤ X ≤ 9). This can be done by finding the cumulative probability up to 9 and then subtracting the cumulative probability up to 5 from it: P(X ≤ 9) - P(X ≤ 5).

Remember that the Poisson distribution assumes that X must be a whole number, and the calculations can often be made using statistical software or a calculator with statistical functions.