SOLUTION: Given that x has a Poisson distribution with mu equals 9, what is the probability that x equals 3?

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Question 1140089: Given that x has a Poisson distribution with mu equals 9, what is the probability that x equals 3?
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the poisson probability formula is:

p(x) = m^x * e^(-m) / x!

m is the mean
x is the desired number that you want the probability for.
e is the scientific constant equal to 2.718281828.....

when m = 9 and x = 3,the formula becomes;

p(3) = 9^3 * e^(-9) / 3! = .01499 rounded to 4 decimal digits.

there is an online calculator that does the dirty work for you.

in addition, that calculator gives you much more than just the probability of exactly x occurrences.

that calculator can be found at https://www.algebra.com/tutors/faq.mpl

here's a display of the results from that calculator dealing with your problem.

here's a reference that tells you what the poisson probability distribution is and how to work with it.

https://stattrek.com/probability-distributions/poisson.aspx

note that the formula, shown as:

p(x) = m^x * e^(-m) / x!

m is the mean
x is the desired number that you want the probability for.
e is the scientific constant equal to 2.718281828.....

can also be shown as:

p(x) = m^x / (e^m * x!)

that's because e^(-m) is the same as 1 / e^m.

note that the calculator not only gives you p(x = 3).

it also gives you p(x < 3), p(x <= 3), p(x > 3), p(x >= 3).

SOLUTION: Given that x has a Poisson distribution with mu equals 9​, what is the probability that x equals 3​?

SOLUTION: Given that x has a Poisson distribution with mu equals 9, what is the probability that x equals 3?