Question

00 points Akron's Children Hospltal has reported that an average of 6 patients arrive in the emergency room each hour. Arrivals at this emergency room are knobn to folow a Poisson probabilily distribut What is the probability that exactly 10 patients will armive in the emergency room between 1:00 pm and 2:00 pm today? T. (Report your answer to 4 decimal places, using conventional rounding rules) What is the probability that no more than 3 patients wil arrive in the emergency room between 6.30 pm and 7:30 pm today (Report your answer to 4 decimal places, using conventional rounding rules) What is the probability that exactly 1 patient will arrive in the emergency room between 11.00 am and 11.30 am today? (Report your answer to 4 decimal places, using conventional rounding rules) t 6 patients armive in the emergency room each hour, what is the variance of this probabity dstritution? (Report your answer to 4 decimal places, using conventional rounding rules)

Answer 1

Solution

given : λ-6/hour or λ-6/60 minutes

let "x" be patients will arrive in the emergemcy room

formula: P)

P(exactly 10) P(X = 10)

P(X 10)10 0.0413

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P(no more than 3) > P(X 3)

$P(X\leq 3)\Rightarrow P(X=0)+P(X=1)+P(X=2)+P(X=3)$

0! 1! 2!

e-6 * 216

{ } 36 216 PlXS3-e-6 . 1+6+

$P(X\leq 3)\Rightarrow e^{-6}*\left \{ 1+6 +18+36\right \}$

3)e

P(X < 3)0.1512

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$\lambda =\frac{6}{2}=\mathbf{3}/30\;minutes$

$P(exactly\;1)\Rightarrow P(X=1)$

$P(X=1)=\frac{e^{-3}*3^{1}}{1!}=\mathbf{{\color{Red} 0.1494}}$

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$Variance=\lambda =\mathbf{{\color{Red} 6}}$