Mathematics: Q, s, t, and u are coplanar: true or false? why?

Q, s, t, and u are coplanar: true or false? why?

chimwim7515

23.04.2022

a) 0.0613 b)0.0803

Step-by-step explanation:

Ms. Bergen estimates that the probability is 0.025 that an applicant will not be able to repay his or her installment loan.

p = 0.025

Let's consider that an applicant is not be able to repay his or her installment loan as a ''success''

p (success) = 0.025

Last month she made 40 loans ⇒ n = 40

For the poisson approximation to the binomial we need to calculate n.p that will be the λ parameter in our poisson approximation

n.p=40.(0.025)=1

λ=n.p=1

Let's rename λ = j

In our poisson approximation :

$f(k,j)=\frac{e^{-j} .j^{k} }{k!}$

f(k,j) is the probability function for our poisson variable where we calculated j,e is the euler number and k is the number of success :

$f(k,1)=\frac{e^{-1} .1^{k} }{k!}$

For a) We are looking the probability of 3 success :

$f(3,1)=\frac{e^{-1} .1^{3} }{3!}=0.0613$

For b) We are looking for the probability of at least 3 success

If ''L'' is the number of success

$P(L\geq 3)=1-P(L\leq 2)$

$P(L\leq 2)=P(L=0)+P(L=1)+P(L=2)$

$P(L\leq 2)=f(0,1)+f(1,1)+f(2,1)$

$P(L\leq 2)=e^{-1} +e^{-1}+\frac{e^{-1}}{2} =e^{-1}(1+1+\frac{1}{2} )$

$P(L\geq 3)=1-P(L\leq 2)=1-e^{-1}(1+1+\frac{1}{2} )=0.0803$

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