Question

MA3000-D2-SU18A-Wiemann Han Quiz: LP04 Computational Quiz Time Remai This Question: 4 pts 11 of 11 (8 complete) Round to four decimal places as needed ) (Round to four decimal places as needed) Enter your answer in each of the answer boxes

Answer 1

Given: lambda = 5.6 formula: P(X = x) = e6- lambda * lambda^x/x! a. P(X = 1) = e^-5.6 * 5.6^1/1! = 0.0207 b. P(X < 1) rightdoublearrow P(X = 0) = e^-5.6 * 5.6^0/0! = 0.0037 c. P(X > 1) rightdoublearrow 1 - P(X lessthanorequalto 1) P(X > 1) = 1 - {P(X = 0) + P(X = 1)} P(X > 1) = 1 - {0.0037 + 0.0207} P(X > 1) = 0.9756 d. P(X lessthanorequalto 1) = P(X = 0) + P(X = 1) P(X lessthanorequalto 1) = 0.0037 + 0.0207 = 0.0244

$\mathbf{given:}\lambda =5.6$

$\mathbf{formula:}P(X=x)=\frac{e^{-\lambda }*\lambda ^{x}}{x!}$

$\mathbf{{\color{Blue} a.}}\;P(X=1)=\frac{e^{-5.6}*5.6^{1}}{1!}={\color{Red} \mathbf{0.0207}}$

$\mathbf{{\color{Blue} b.}}\;P(X<1)\Rightarrow P(X=0)=\frac{e^{-5.6}*5.6^{0}}{0!}={\color{Red} \mathbf{0.0037}}$

$\mathbf{{\color{Blue} c.}}\;P(X>1)\Rightarrow1- P(X\leq 1)$

$P(X>1)=1-\left \{ P(X=0) +P(X=1)\right \}$

$P(X>1)=1-\left \{ 0.0037 +0.0207\right \}$

$P(X>1)={\color{Red} \mathbf{0.9756}}$

$\mathbf{{\color{Blue} d.}}\;P(X\leq 1)= P(X=0) +P(X=1)$

$P(X\leq 1)= 0.0037+0.0207={\color{Red} \mathbf{0.0244}}$