Answer to Question #343313 in Statistics and Probability for cat

Question #343313

The mean number of births per minute in a country in a recent year was about nine. Find the probability that the

number of births in any given minute is (a) exactly six, (b) at least six, and (c) more than six.


1
Expert's answer
2022-05-24T17:47:27-0400

Let X=X= the number of births : XPo(λ).X\sim Po(\lambda).

Given λ=9.\lambda=9.

(a)


P(X=6)=e9(9)66!=0.09109P(X=6)=\dfrac{e^{-9}(9)^6}{6!}=0.09109

(b)


P(X6)=1P(X=0)P(X=1)P(X\ge6)=1-P(X=0)-P(X=1)

P(X=2)P(X=3)-P(X=2)-P(X=3)

P(X=4)P(X=5)-P(X=4)-P(X=5)

=1e9(9)00!e9(9)11!=1-\dfrac{e^{-9}(9)^0}{0!}-\dfrac{e^{-9}(9)^1}{1!}

e9(9)22!e9(9)33!-\dfrac{e^{-9}(9)^2}{2!}-\dfrac{e^{-9}(9)^3}{3!}

e9(9)44!e9(9)55!=0.88431-\dfrac{e^{-9}(9)^4}{4!}-\dfrac{e^{-9}(9)^5}{5!}=0.88431

(c)


P(X>6)=P(X6)P(X=6)P(X>6)=P(X\ge 6)-P(X=6)

=0.79322=0.79322


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