Question

In analyzing hits by certain bombs in a​ war, an area was partitioned into 556 ​regions, each with an area of 0.45 km2. A total of 545 bombs hit the combined area of 556 regions. Assume that we want to find the probability that a randomly selected region had exactly two hits. In applying the Poisson probability distribution​ formula, ​P(x)=μ^x * e^-μ/ x!​, identify the values of μ​, ​x, and e. ​Also, briefly describe what each of those symbols represents.

Answer 1

Answer:

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

There is a 18.03% probability that a randomly selected region had exactly two hits.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given interval.

In this problem we have that:

A total of 545 bombs hit the combined area of 556 regions. So the mean hits per region is:

$P = \frac{545}{556} = 0.9802$

Assume that we want to find the probability that a randomly selected region had exactly two hits.

This is P(X = 2).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 2) = \frac{e^{-0.9802}*(0.9802)^{2}}{(2)!} = 0.1803$

There is a 18.03% probability that a randomly selected region had exactly two hits.