x is 3 that is the number of hits
e = 2.71828 is the Euler number
μ is the mean in the given interval = 0.967
There is 5.72% probability that a randomly selected region had exactly three hits.
Let X be the random variable denoting the number of bombs hitting the selected sample.
The following formula determines the likelihood that x in a Poisson distribution corresponds to the number of successes of a random variable.
P(X = x) = e^₋μ × μˣ / (x)!
Here, X is the random variable denoting the number of bombs hitting the selected sample.
μ is the mean number of hits per region.
e is the constant value.
Since 535 bombs struck a total of 553 regions, the ratio of strikes per region to the total number of regions is 535 to 553.
μ = 535 / 553
μ = 0.967
Assume that we want to find the probability that a randomly selected region had exactly 3 hits.
which means, P(X = 3)
P(X = x) = e^₋μ × μˣ / (x)!
P(X = 3) = e^₋0.967 × (0.967)³/ (3)!
= 0.057
There is approximately 5.72% probability that a randomly selected region had exactly three hits.
Your question was incomplete. Please find the missing content here.
In analyzing hits by certain bombs in a war, an area was partitioned into 553 regions, each with an area of 0.95 km². A total of 535 bombs hit the combined area of regions. Assume that we want to find the probability that a randomly selected region had exactly 3 hits.In applying the Poisson probability distribution formula, P(X) = e^₋μ × μˣ / (x)!, identify the values of μ, x and e. Also , briefly describe what each of those symbols represent.
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