2.According to www.city-data, the mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000. Check the three assumptions associated with the Central Limit Theorem. What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009

Answers

Answer 1

Answer:

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean price for a detached house in Franklin County, OH in 2009 was $192,723. Suppose we know that the standard deviation was $42,000.

This means that [tex]\mu = 192723, \sigma = 42000[/tex]

Sample of 75:

This means that [tex]n = 75, s = \frac{42000}{\sqrt{75}}[/tex]

What is the probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009?

1 subtracted by the p-value of Z when X = 190000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{190000 - 192723}{\frac{42000}{\sqrt{75}}}[/tex]

[tex]Z = -0.56[/tex]

[tex]Z = -0.56[/tex] has a p-value of 0.2877

1 - 0.2877 = 0.7123

0.7123 = 71.23% probability that a random sample of 75 detached houses in Franklin County had a mean price greater than $190,000 in 2009.


Related Questions

The absolute value inequality equation |2x – 1| > 3 will have what type of solution set?

Answers

Given:

The inequality is:

[tex]|2x-1|>3[/tex]

To find:

The solution set for the given inequality.

Solution:

We know that, if [tex]|x|>a[/tex], then [tex]x<-a[/tex] and [tex]x>a[/tex].

We have,

[tex]|2x-1|>3[/tex]

It can be written as:

[tex]2x-1<-3[/tex] or [tex]2x-1>3[/tex]

Case I:

[tex]2x-1<-3[/tex]

[tex]2x<-3+1[/tex]

[tex]2x<-2[/tex]

[tex]x<\dfrac{-2}{2}[/tex]

[tex]x<-1[/tex]

Case II:

[tex]2x-1>3[/tex]

[tex]2x>3+1[/tex]

[tex]2x>4[/tex]

[tex]x>\dfrac{4}{2}[/tex]

[tex]x>2[/tex]

The required solution for the given inequality is [tex]x<-1[/tex] or [tex]x>2[/tex]. The solution set in the interval notation is [tex](-\infty,-1)\cup (2,\infty)[/tex].

Therefore, the required solution set is [tex](-\infty,-1)\cup (2,\infty)[/tex].

What is the slope? Please Help

Answers

Answer:

-1

Step-by-step explanation:

Pick two points on the line

(0,2) and (2,0)

Using the slope formula

m = ( y2-y1)/(x2-x1)

    = ( 0-2)/(2-0)

    = -2/2

  = -1

Answer:

-1

Step-by-step explanation:

Use two points on the line to find the slope, using rise over run.

We can use the points (0, 2) and (2, 0).

From the first point to the other, the y value decreases by 2 and the x value increases by 2.

Use rise (change in y value) over run (change in x value):

-2 / 2

= -1

So, the slope is -1.

help whats the volume of this

Answers

Answer:

93.6

Step-by-step explanation:

The easiest way for me to complete this was to break it up into parts. I Separated the small triangle and the big triangle. I turned them both into squares and multiplied the dimensions. I then divided those by two and added them together.

The graph of the function f(x) = (x + 2)(x + 6) is shown below.

On a coordinate plane, a parabola opens up. It goes through (negative 6, 0), has a vertex at (negative 4, negative 4), and goes through (negative 2, 0).

Which statement about the function is true?

The function is positive for all real values of x where
x > –4.
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.

Answers

Answer:

2nd option,

The function is negative for all read values of x where -6<x<-2

The function f(x) = (x + 2)(x + 6) is a quadratic function, and the function is negative for all real values of x where –6 < x < –2.

What are quadratic functions?

Quadratic functions are functions that have an exponent or degree of 2

The function is given as:

f(x) = (x + 2)(x + 6)

From the graph of the function, the vertex is at (-4,-4) and the x-intercepts are at x = -6 and x = -2

Since the vertex is minimum, then the function is negative for all real values of x where –6 < x < –2.

Read more about x-intercepts at:

https://brainly.com/question/3951754

16.Brendan practiced soccer for 12 hours on Monday, 1 hours on
Tuesday, 14 hours on Wednesday, and hour on Thursday in
preparation for the game on Friday. How many total hours did
Brendan practice soccer in this week

Answers

Answer:

27

Step-by-step explanation:

A capark has 34 rows and each row can acommodate 40 cars. If there are 976 cars parked, how many cars can still be parked?​

Answers

Answer:

384 cars

Step-by-step explanation:

To find the total number of spaces in the carpark, we must multiply the number of rows by how many cars they can accommodate:

34 ⋅ 40 = 1360

As you can see, we have 1360 total spaces. Since there are 976 cars parked, and we want to find out how many spaces are left, we have to subtract the amount of cars parked from the total spaces.

1360 - 976 = 384

Therefore, our answer is 384, specifically, 384 cars.

Answer:

384 cars.

Step-by-step explanation:

40 * 34 - 976

= 1360 - 976

= 384.

Plz help me find x and y on the triangle big thanks​

Answers

Answer:

This is a 30-60-90 right triangle.

The ratio of sides:

a : b : c = 1 : √3 : 2

Compare with the given values:

a = 3√3, b = y, c = xy = 3√3*√3 = 9x = 2*3√3 = 6√3

Question 17 and 18 plz show ALL STEPS and HELP ME ASAP

Answers

Answer:

17) 750/9 and 18) 364

Step-by-step explanation:

17. Summation of 75*(0.1)^i from i=0 to infinity, that is equal to 75*(Summation of (0.1)^i). Summation of (0.1)^I is a geometric series with a sum of 1/(0.9)=10/9. Hence the series have a sum equal to 75*(10/9)=750/9

18) It's a series with sum=1+3+9+27+81+243=364

Find the surface area of a cube that has side length of 3.5 inches

Answers

Answer:

73.5

Step-by-step explanation:

find the range of the function f (x) = 2x + 5 for the domain 2,5,7

Answers

Answer:

The range is {9,15,19}  

Step-by-step explanation:

f (x) = 2x + 5

Let x = 2

f (2) = 2*2 + 5 = 4+5 = 9

Let x = 5

f (5) = 2*5 + 5 = 10+5 = 15

Let x = 7

f (7) = 2*7 + 5=14+5 = 19

The domain is {2,5,7}

The range is {9,15,19}  

Answer:

i think what you wrote is that the domain is 2 to 5.7.

so you plug in these two numbers inside the equation cause domain means the distance in the x axis so this is how it goes.

2(2) + 5 = 9

2(5.7) +5= 16.4

so the range is 9 to 16.4

hope that answers your question...






[tex] \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} = what[/tex]



Answer I'll make and mark as brainlist.

Answer Fast.
Post on - 2 Aug 2021 ​

Answers

2^3
——
3^3



............

[tex]f(x)=e^{3x} .sinx[/tex] . tính [tex]d^{2} f(0)[/tex]

Answers

Answer:

6

Step-by-step explanation:

đạo hàm cấp 2 của f(x) rồi thế 0 vào

Multiply (2x-5)(x+3)

Answers

Answer:

2x^2+x-15

Step-by-step explanation:

foil

Answer:

2x^2 + x - 15

Step-by-step explanation:

using FOIL

(2x - 5)(x + 3)

[(2x ⋅ x) + (2x ⋅ 3) + (-5 ⋅ x) + (-5 ⋅ 3)]

[2x^2 + 6x - 5x - 15]

2x^2 + x - 15

Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)
(x − 1)y'' − xy' + y = 0, y(0) = −7, y'(0) = 3

Answers

You're looking for a solution of the form

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n[/tex]

Differentiating twice yields

[tex]\displaystyle y' = \sum_{n=0}^\infty n a_n x^{n-1} = \sum_{n=0}^\infty (n+1) a_{n+1} x^n[/tex]

[tex]\displaystyle y'' = \sum_{n=0}^\infty n(n-1) a_n x^{n-2} = \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n[/tex]

Substitute these series into the DE:

[tex]\displaystyle (x-1) \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n - x \sum_{n=0}^\infty (n+1) a_{n+1} x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^{n+1} - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=0}^\infty (n+1) a_{n+1} x^{n+1} + \sum_{n=0}^\infty a_n x^n = 0[/tex]

[tex]\displaystyle \sum_{n=1}^\infty n(n+1) a_{n+1} x^n - \sum_{n=0}^\infty (n+1)(n+2) a_{n+2} x^n \\\\ \ldots \ldots \ldots - \sum_{n=1}^\infty n a_n x^n + \sum_{n=0}^\infty a_n x^n = 0[/tex]

Two of these series start with a linear term, while the other two start with a constant. Remove the constant terms of the latter two series, then condense the remaining series into one:

[tex]\displaystyle a_0-2a_2 + \sum_{n=1}^\infty \bigg(n(n+1)a_{n+1}-(n+1)(n+2)a_{n+2}-na_n+a_n\bigg) x^n = 0[/tex]

which indicates that the coefficients in the series solution are governed by the recurrence,

[tex]\begin{cases}y(0)=a_0 = -7\\y'(0)=a_1 = 3\\(n+1)(n+2)a_{n+2}-n(n+1)a_{n+1}+(n-1)a_n=0&\text{for }n\ge0\end{cases}[/tex]

Use the recurrence to get the first few coefficients:

[tex]\{a_n\}_{n\ge0} = \left\{-7,3,-\dfrac72,-\dfrac76,-\dfrac7{24},-\dfrac7{120},\ldots\right\}[/tex]

You might recognize that each coefficient in the n-th position of the list (starting at n = 0) involving a factor of -7 has a denominator resembling a factorial. Indeed,

-7 = -7/0!

-7/2 = -7/2!

-7/6 = -7/3!

and so on, with only the coefficient in the n = 1 position being the odd one out. So we have

[tex]\displaystyle y = \sum_{n=0}^\infty a_n x^n \\\\ y = -\frac7{0!} + 3x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots[/tex]

which looks a lot like the power series expansion for -7.

Fortunately, we can rewrite the linear term as

3x = 10x - 7x = 10x - 7/1! x

and in doing so, we can condense this solution to

[tex]\displaystyle y = 10x -\frac7{0!} - \frac7{1!}x - \frac7{2!}x^2 - \frac7{3!}x^3 - \frac7{4!}x^4 + \cdots \\\\ \boxed{y = 10x - 7e^x}[/tex]

Just to confirm this solution is valid: we have

y = 10x - 7   ==>   y (0) = 0 - 7 = -7

y' = 10 - 7   ==>   y' (0) = 10 - 7 = 3

y'' = -7

and substituting into the DE gives

-7 (x - 1) - x (10 - 7) + (10x - 7 ) = 0

as required.

3. Find F(3).
F(x)=-x^3+4x^2-2x

Answers

Answer:

To Find F(3) you just have to replace x=3 so:

F(3)= -3^3 + 4×3^2 -2×3 = -27 +4×9 - 6 = -33 + 36 = 3

The length of a rectangular field is 25 m more than its width. The perimeter of the field is 450 m. What is the actual width and length?

Answers

Answer:

length= 125

width= 100

Step-by-step explanation:

let width have a length of x m

therefore length= (x+25)m

perimeter=2(length +width)

p=2((x+25)+x)

p=4x+50

but we have perimeter to be 450,, we equate it to 4x+50 above,

450=4x+50

4x=400

x=100 m

length= 125

width= 100

Solve the equation by factoring: 5x^2 - x = 0

Answers

Answer:

Step-by-step explanation:

x = 0, 1/5

in the given circle the radius is 9 cm what is its diameter?​

Answers

Answer:

18

Step-by-step explanation:

The diameter is equal to twice the length of the radius

So if the radius is 9 then the diameter is 9 * 2 = 18

Based on what we have learned, how can we ensure that we choose a sample of students that is representative of all 8:00 AM classes that take place on a given morning

Answers

Sampling technique is a way of selecting a sample from a given population. The best way to get a sample of students that represents all 8:00 AM classes is by using a stratified sampling technique.

From the complete question, we can summarize the given data as follows:

[tex]Buildings = 3[/tex] ----3 buildings in the college

[tex]Lecture\ Halls =2[/tex]  ---- 2 lecture halls in each building

[tex]Capacity = 100[/tex] --- 100 students in each lecture hall

Because the students' lecture halls are not in the same building, the best way to get a sample is as follows:

Divide the students into groups (In this case, the students will be grouped by the buildings of their lecture halls)

The number of students in each building is:

[tex]Students = Capacity \times Lecture\ Halls[/tex]

[tex]Students = 100 \times 2[/tex]

[tex]Students = 200[/tex]

There are 200 students in each building

Then select at random an equal proportion of student from each building (say 30 students in each building)

The above method is referred to as a stratified sampling technique because the population of the students are divided into groups, before being randomly selected.

Read more about sampling techniques at:

https://brainly.com/question/9612230

If Damien does a job in 21 hours less time than Caitlyn, and they can do the job together in 14 hours, how
long will it take each to do the job alone?

Answers

Answer: Damien = 7.5 hours and Caitlyn = 28.5 hours

Step-by-step explanation:

Damien = X -21

Caitlyn = X

2X - 21 = 14

2X = 14 + 21

X = (14+21)/2

X = 7.5

The sum of two consecutive even integers is 54. What are the two integers?

Answers

Answer:

26 and 2

Step-by-step explanation:

Given,

Sum of two even numbers = 54

let one number be x

another number be x +2

x + x +2 = 54

2x + 2 = 54

2x = 54 - 2

2x = 52

x = 52/2

x = 26

Therefore, the numbers are 26 and 26 + 2 = 28..

which one of these points lies on the line described by the equation below y - 5 = 6 ( x - 7 )

Answers

Answer:

the answer would be (7,5)

A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player?

Answers

The lowest he will get is 10 points and highest 15, 3-2=1 so minimum increment is 1. Count 10 to 15 by increment of 1 you will have 6 different numbers.

The LARGEST angle has a measure of ______degrees

Answers

Answer:

90 i think

Step-by-step explanation:

Which expression is equivalent to the given expression?

Answers

Answer:

a³b

Step-by-step explanation:

(ab²)³/b⁵

= a³b⁶/b⁵

= a³b

John and mike got paid $40.00 for washing
car. John work one hour, mike worked 1.5 hrs.
How much do they get paid for time worked?

Answers

This question is incomplete , l can’t answer it . You have to say how much minutes or hours they work to get paid $40 ,if you just say that John’s work one hour and Mike work 1.5 hours then I don’t know what to solve ,this question is a complete

If you were to place $2,500 in a savings account that pays 3% interest
compounded continuously, how much money will you have after 5 years?
Assume you make no other deposits or withdrawals.

Answers

Answer:

$2904.59

Step by Step Explanation:

Find m<1.
33°
47°
42°
28°

Answers

Answer:

<1 = 33

Step-by-step explanation:

The sum of the angle of a triangle is 180

31+116+x = 180

x+147=180

x = 180-147

x = 33

Graph x^2/49+y+1^2/4=1

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Perhaps you want a graph of ...

  x^2/49 +(y +1)^2/4 = 1

This is an ellipse centered at (x, y) = (0, -1) with a major axis in the x-direction of 14, and a minor axis in the y-direction of 4.

If 8 bags of chips cost 10.32;how much will you pay for 20 bags?

Answers

Answer:

$25.80

Step-by-step explanation:

First, let's find the cost of one bag of chip:

10.32/8 = 1.29

If one bag costs $1.29, simply multiply the number of bags (20) by 1.29

1.29 x 20 = 25.80

               = $25.80

Answer:

25.80

Step-by-step explanation:

We can use a ratio to solve

8 bags             20 bags

-------------   = ----------------

10.32               x dollars

Using cross products

8x = 10.32 * 20

8x =206.40

Divide each side by 8

8x/7 = 206.40/8

x =25.80

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