1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elenna [48]
3 years ago
13

Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 t

hat an applicant will not be able to repay his or her installment loan. Last month she made 40 loans. Use the poisson approximation to the binomial.
a. What is the probability that three loans will be defaulted?
b. What is the probability that at least 3 loans will be defaulted?
Mathematics
1 answer:
ddd [48]3 years ago
3 0

Answer:

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

You might be interested in
Five of the 25 girls on Alden Middle School’s soccer team are seventh-grade students. Find the percentage of seventh graders on
Fed [463]

Oh, I remember this one. Here's this if you need it, if it doesn't help then let me know.

6 0
3 years ago
72 = 8 x 9
vivado [14]
8988989889 IDK hate doing the it but luv getting the answers
8 0
3 years ago
Read 2 more answers
Can someone help with #4<br><br> 15 points
BigorU [14]

I would check my math but 4/3 = 1.3 x 18= 24 divided by 2 for radius would be 12x12=144 x pie or 3.14 would be 452.16

4 0
3 years ago
Two kinds of tickets to an outdoor concert were sold: lawn tickets and seat tickets. Less than 400 tickets in total were sold. L
miskamm [114]

Answer:

Tickets to sit on the bench (b) = 150

Tickets to sit on the lawn (l) = 200

Step-by-step explanation:

Tickets to sit on a bench (b)cost $75 each.

Tickets to sit on the lawn (l) cost $40 each

350 tickets had been sold

$19,250 had been raised through tickets sales

This forms a simultaneous equation:

b + l = 350 ... (i)

75b + 40l = 19,250 ... (ii)

Multiplying (i) by 40 and (ii) by 1 we get;

40b + 40l = 14,000 ... (i)

75b + 40l = 19,250 ... (ii)

Subtracting (ii) - (i) we get;

35b = 5250

b = 5250 ÷ 35 = 150

7 0
3 years ago
Please help me i really need help please please
gizmo_the_mogwai [7]

Answer:

it's D all of the above

Step-by-step explanation:

.......

7 0
2 years ago
Read 2 more answers
Other questions:
  • Mike ate 1 3 of a bag of peanuts at the game, and on the way home he ate 1 3 of what was left. How much of the bag of peanuts di
    5·1 answer
  • A triangle has one angle that measures 90° and another that measures 20°. what kind of triangle is it?
    12·1 answer
  • What is 5256 divided by 52
    14·1 answer
  • A culture started with 5000 bacteria. after 7 hours, it grew to 6500 bacteria. predict how many bacteria will be present after 1
    10·1 answer
  • PLS HELP (LAST QUESTION)
    15·1 answer
  • Find the area of the following figure and choose the appropriate result.
    7·1 answer
  • Find the inverse function of y=3x-7
    15·1 answer
  • What is another way to name the plane ACE?
    5·2 answers
  • Find the value of X and y in this figure
    6·1 answer
  • Identify the type of sampling method used.A trucking company places their office phone number on the back of all of their vehicl
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!