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
inysia [295]
3 years ago
9

The Washington, DC, region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure

during the one-year period ending in February 2008 (The Washington Post, June 19, 2008). Over the past year, the number of foreclosures per 10,000 homes is 131 for the Washington area, while it is 87 nationally. In other words, the foreclosure rate is 1.31% for the Washington, DC area and 0.87% for the nation. Assume that the foreclosure rates remain stable.
Required:
a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?
b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?
c. Comment on the above findings.
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
7 0

Answer:

a) 0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b) 0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c) The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

Step-by-step explanation:

For each home, there are only two possible outcomes. Either it goes into foreclosure, or it does not. The probability of a home going into foreclosure is independent of other homes. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

a. What is the probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure?

The foreclosure rate is 1.31% for the Washington, DC area, which means that p = 0.0131

We wanto to find, with n = 100:

P(X < 2) = P(X = 0) + P(X = 1)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0131)^{0}.(0.9869)^{100} = 0.2675

P(X = 1) = C_{100,1}.(0.0131)^{1}.(0.9869)^{99} = 0.3551

P(X < 2) = P(X = 0) + P(X = 1) = 0.2675 + 0.3551 = 0.6226

0.6226 = 62.26% probability that in a given year, fewer than 2 out of 100 houses in the Washington, DC area will go up for foreclosure.

b. What is the probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure?

Foreclosure rate of 0.87% for the nation, which means that p = 0.0087. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{100,0}.(0.0087)^{0}.(0.9913)^{100} = 0.4174

P(X = 1) = C_{100,1}.(0.0087)^{1}.(0.9913)^{99} = 0.3663

P(X < 2) = P(X = 0) + P(X = 1) = 0.4174 + 0.3663 = 0.7837

0.7837 = 78.37% probability that in a given year, fewer than 2 out of 100 houses in the nation will go up for foreclosure.

c. Comment on the above findings.

The proportion of foreclosures in the Nation is lower than in Washington, which means that with a sample size of 100, it is likely to have a small number(fewer than 2) of foreclosures than Washington DC.

You might be interested in
Find the 75th term of the arithmetic sequence -1, 15, 31, ...−1,15,31,...
Readme [11.4K]

Answer:

1183

Step-by-step explanation:

Common difference:

d = 31 - 15 = 16

nth term:

a_n = a_1 + (n - 1)d

Here, a_1 = -1

a_{75} = -1 + (75 - 1)(16)

a_{75} = 1183

3 0
2 years ago
Can someone solve these for me
tatuchka [14]

Answer:

0.66 and 33/50

62.5% and 5/8

0.75 and 3/4

120% and 1 1/5

0.005 and 1/200

3.75 and 375%

I hope that is correct and helps you! :)

Step-by-step explanation:

8 0
3 years ago
Multiply. Write your answer in simplest form.
Mariana [72]

Answer:

The answer in lowest terms is 15/17

Step-by-step explanation:

Hope that helps!

3 0
2 years ago
How much is 3 over 15 plus 1 over 3
REY [17]

Answer:

8/15

Step-by-step explanation:

Well to add fractions you have to have the same denominator so you would multiply your 1/3 by 5 to be 5/15 then you can add.

3/15 + 5/15 = 8/15

4 0
3 years ago
Read 2 more answers
In plane ABC the measure of angle A equals 42° the measure of angle B is five times the measure of angle C find the measure of a
krok68 [10]

Step-by-step explanation:

I think what is meant in the triangle ABC we have the three angles.

the sum of all angles in a triangle is airways 180 degrees.

so,

180 = A + B + C

180 = 42 + B + C

now, we know also that

B = 5×C

so, we can use that above

180 = 42 + 5×C + C

138 = 6×C

C = 138/6 = 23 degrees

B = 5×C = 5×23 = 115 degrees

7 0
2 years ago
Other questions:
  • Jeff's dog weighs 76 pounds what is the <br> Dog's weight rounded to the nearest ten pounds
    9·1 answer
  • 12 pencils can be purchased with $3. How many pencils can be purchased with $4.50? pencils
    13·2 answers
  • sara wants to buy a necklace. the necklace has a list pice of $41 and the saels tax is 6%what will be the cost of the necklace a
    11·2 answers
  • 2.what is three hundred sixty four thousandths in decimal form
    5·2 answers
  • How do I solve this?
    9·2 answers
  • Twice as many as points as bob
    5·1 answer
  • Drew is holding a fund-raiser. He is taking donations from his family members to supports a charity. Each family member donates
    5·1 answer
  • (8.75-2.16)÷7.1+(4.5+1.3)÷4.3
    14·2 answers
  • C
    11·1 answer
  • Solve the equation for all real solutions in simplest form.<br> -4m^2+2m-11=-5m^2
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!