8.92% probability that there are exactly 3 crimes during the next hour
The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:
P( X = x ) = [ e⁻ᵃ × aˣ ] / x!
Where a is the mean in the given time interval,
x is the number of successes, and the Euler number e = 2.71828.
In a city with 30000 people, each person has a 0.00020 probability of committing a crime each hour.
So,
a = 30000 × 0.00020
a = 6
The probability that there are exactly 3 crimes during the next hour will be:
P( X = x ) = [ e⁻ᵃ × aˣ ] / x!
P(X = 3) = [ e⁻⁶ × 6³ ] / 3!
P( X = 3 ) = [ (2.71828)⁻⁶ × 6³ ] / 3!
P( X = 3 ) = [ 0.00247876218 × 216 ] / 3!
P ( X = 3 ) = 0.53541263103 / 6
P ( X = 3 ) = 0.0892354385
8.92% probability that there are exactly 3 crimes during the next hour.
Learn more about probability here:
brainly.com/question/13604758
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