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
Every weekend me and my brother and my cousin go outside to play basketball and when i was the one who will shoot the ball to th
Rus_ich [418]

Answer:

10 . 44 ft

Step-by-step explanation:

sin 50 = opposite leg / hypotenuse = 8 / x

8 / sin 50 = x    = 10 .44  ft

6 0
2 years ago
Read 2 more answers
Someone help pls!!! Idk what it is
Hitman42 [59]

Answer:

first option

2^(1/6)

Step-by-step explanation:

= 2^(1/2) * 2^(1/3)

= 2^(1/6)

6 0
3 years ago
Use the correct order of operations to calculate5 1/2 * 4 1/2 -7/2/ 2 1/3​
IgorC [24]
If there are multiple operations at the same level on the order of operations off from left to right and you work like this first noticed that there are no parentheses or exponents so we moved to multiplication and division with any sense of parentheses
5 0
3 years ago
Read 2 more answers
mark bought 168 meters of fencing to enclose an area of pasture for his sheep. he plans to use all of the fencing to make a rect
Anika [276]
The two long sides are 63meters and the shorter sides are 21meters.
7 0
3 years ago
Read 2 more answers
Hay dos veces la cantidad de manzanas que naranjas en un puesto de frutas. Después de que se vendieron 15 naranjas, hay tres vec
Nastasia [14]

Answer:

45

Step-by-step explanation:

4 0
3 years ago
Other questions:
  • Determine whether the following is an expression or an equation. -4+5-2=10x
    9·1 answer
  • According to Piaget, adolescents have entered the final stage of cognitive development. The _____ stage enables adolescents to t
    15·1 answer
  • Circle A is congruent to circle J. Chords BC, CF, EG, KL, LO, and MP are congruent.
    6·2 answers
  • Simplify 8 over negative 4 divided by negative 3 over 9.
    10·1 answer
  • Gimme some relaxation songs​
    6·2 answers
  • What is the product of (–22.1)(–5.6)?
    6·1 answer
  • Find the value of x.
    12·2 answers
  • A side of square B is four times the length of a side of square A. How many times greater is the area of square B than the area
    5·1 answer
  • Need help now please please
    9·1 answer
  • 2 hermanos tienen una cuenta de ahorros en el banco por 1.920.000 pesos, lo que le corresponde al hermano mayor es 6 veces lo qu
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!