The sizes of houses in Kenton County are normally distributed with a mean of 1346
square feet with a standard deviation of 191 square feet. For a randomly selected
house in Kenton County, what is the probability the house size is:
a. over 1371 square feet?
O Z=
o probability =
b. under 1296 square feet?
O Z=
o probability =
c. between 773 and 1637 square feet?
o zl =
o Z2 =
o probability =
Note: Z-scores should be rounded to 2 decimal places & probabilities should be
rounded to 4 decimal places.
License
Points possible: 8
This is attempt 1 of 3.
Answers
Answer:
(a) The probability that the house size is over 1371 square feet is 0.4483.
(b) The probability that the house size is under 1296 square feet is 0.3974.
(c) The probability that the house size is between 773 and 1637 square feet is 0.9344.
Step-by-step explanation:
We are given that the sizes of houses in Kenton County are normally distributed with a mean of 1346 square feet with a standard deviation of 191 square feet.
Let X = the sizes of houses in Kenton County
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean size of houses = 1346 square feet
[tex]\sigma[/tex] = standard deviation = 191 square feet
(a) The probability that the house size is over 1371 square feet is given by = P(X > 1371 square feet)
P(X > 1371) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{1371-1346}{191}[/tex] ) = P(Z > 0.13) = 1 - P(Z [tex]\leq[/tex] 0.13)
= 1 - 0.5517 = 0.4483
The above probability is calculated by looking at the value of x = 0.13 in the z table which has an area of 0.5517.
(b) The probability that the house size is under 1296 square feet is given by = P(X < 1296 square feet)
P(X < 1296) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{1296-1346}{191}[/tex] ) = P(Z < -0.26) = 1 - P(Z [tex]\leq[/tex] 0.26)
= 1 - 0.6026 = 0.3974
The above probability is calculated by looking at the value of x = 0.26 in the z table which has an area of 0.6026.
(c) The probability that the house size is between 773 and 1637 square feet is given by = P(773 square feet < X < 1637 square feet)
P(773 < X < 1637) = P(X < 1637) - P(X [tex]\leq[/tex] 773)
P(X < 1637) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{1637-1346}{191}[/tex] ) = P(Z < 1.52) = 0.9357
P(X [tex]\leq[/tex] 773) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{773-1346}{191}[/tex] ) = P(Z [tex]\leq[/tex] -3) = 1 - P(Z [tex]\leq[/tex] 3)
= 1 - 0.9987 = 0.0013
The above probabilities are calculated by looking at the value of x = 1.52 and x = 3 in the z table which has an area of 0.9357 and 0.9987 respectively.
Therefore, P(773 square feet < X < 1637 square feet) = 0.9357 - 0.0013 = 0.9344.
Related Questions
Which of the following has the largest value?
1/2 0.09 35%
Answers
Answer:
1/2
Step-by-step explanation:
its j the biggest its not that hard
Find the Autocorrelation function of the following periodic function: X(t) = A sin(wt +θ) 21 With T=2π/w the period, A, θ, and w are constants.
Answers
Answer:
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
Step-by-step explanation:
To find Autocorrelation function of the following periodic function
Given that:
X(t) = A sin(wt +θ)
with the period T=2π/w , A, θ, and w are constants.
The autocorrelation function of periodic function with period and phase θ can be expressed as:
[tex]R(\tau) = \dfrac{1}{T} \int \limits ^{T/2}_{-T/2} x(t) *x(t - \tau) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{T} \int \limits ^{T/2}_{-T/2} \ A sin ( \omega t + \theta)*A sin [ \omega (t- \tau ) + \theta] \ dt[/tex]
where;
[tex]sinAsin B = \dfrac{1}{2}[cos (A-B) -cos (A+B)][/tex]
Then;
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( \omega t- \omega \tau + \theta - \omega t - \theta) - cos (\omega t - \omega \tau + \theta + \omega t + \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) - cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits ^{T/2}_{-T/2} \ cos ( - \omega \tau ) \ dt - \dfrac{1}{2T} \int \limits ^{T/2}_{-T/2} cos (2 \omega t - \omega \tau + 2 \theta) \ dt[/tex]
The term 2 is the cosine wave of frequency and the phase = [tex]- w \tau + 2 \theta[/tex]
if we integrate that, the second term in the expansion for R(t) = zero
As such,
[tex]R(\tau) = \dfrac{A^2}{2T} \int \limits^{T/2}_{-T/2} \ cos ( - \omega \tau ) dt[/tex]
where ;
[tex]cos (-\omega \tau )[/tex]is constant
Then :
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) [t]^{T/2}_{-T/2}[/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{T}{2}+ \dfrac{T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times [\dfrac{2T}{2}][/tex]
[tex]R(\tau) = \dfrac{A^2}{2T} cos (-\omega \tau) \times T[/tex]
[tex]R(\tau) = \dfrac{A^2}{2} cos (-\omega \tau)[/tex]
since [tex]cos (-\omega \tau) = cos (\omega \tau)[/tex]
[tex]\mathbf{R(\tau) = \dfrac{A^2}{2} cos (\omega \tau)}[/tex]
Find the quotient of 9216 and 150
Answers
Answer: 61.44
Step-by-step explanation:
To find the quotient of 9216 and 150, it means to divide.
9216/150=61.44
Work the following area application problem.
You wish to paint a storage shed. Its four walls measure 5 ft. high and 8 ft. wide each. If one gallon of paint covers 160
sq. ft., how many gallons of paint will you need?
Gallons of paint required =
a. 1
b. 2
c. 3
d. 4
Answers
Answer: a. 1
Step-by-step explanation:
There are 4 walls in total, and each wall measures 5ft high, 8ft wide
5 × 8=40 ft² for each wall
4×40=160 ft² for 4 walls
------------------
stated one gallon cover 160 ft²
160 ÷ 160=1 gallon
Hope this helps!! :)
Please let me know if you have any question
You are contacted by the top cookie-selling Girl Scout troop in the city. As part of their sales plan for next year’s cookie selling season, they need to know (with 99% confidence, or α = 0.01) if the types of cookies purchased by their customers depends on where the scouts sell them. Here is their confidential sales data from last year:
Answers
Answer:
The types of cookies purchased by the customers depends on where the scouts sell them.
Step-by-step explanation:
The data provided is:
Sales Type of Cookie Sold
Method
Thin Mints Tagalongs Do-si-dos Trefoils Samoas
At
parents’ 472 641 350 223 401
workplace
Door
-to- 840 1092 673 511 542
Door
Community 683 742 491 420 374
Events
A Chi-square test for goodness of fit will be used to determine whether the types of cookies purchased by the customers depends on where the scouts sell them.
The hypothesis can be defined as:
H₀: The observed frequencies are same as the expected frequencies.
Hₐ: The observed frequencies are not same as the expected frequencies.
The test statistic is given as follows:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}[/tex]
The formula to compute the expected frequency is:
[tex]E_{i}=\frac{i^{th}\ \text{Row Total}\times i^{th}\ \text{Column Total}}{N}[/tex]
Consider the Excel output for the expected frequency values.
The Chi-square test statistic value is:
[tex]\chi^{2}=\sum\limits^{n}_{i=1}\frac{(O_{i}-E_{i})^{2}}{E_{i}}=56.788[/tex]
The degrees of freedom is:
df = (r - 1)(c - 1)
= (3 - 1)(5 - 1)
= 2 × 4
= 8
The p-value is:
[tex]P(\chi^{2}_{8}>56.788)<0.00001[/tex]
*Use a Chi-square table.
The p-value of the test is very small.
The null hypothesis will be rejected at 1% level of significance.
Conclusion:
There is enough evidence to support the claim that the types of cookies purchased by the customers depends on where the scouts sell them.
Beatrice has 0.26 in her pocket. What percent of a dollar does Beatrice have?
28%
Answers
Answer:
26%
Step-by-step explanation:
If 1 dollar is 100%
Then 0.26 dollar is:
0.26*100= 26%For the following study identify the sources of sampling bias and describe how it might affect the study and conclusion and how you might alter the sampling method to avoid the bias.A nutritionist is interested in the eating habits of college students and observes what each student who enters a dining hall between 8:00 A.M. and 8:30 A.M. chooses for breakfast on a Monday morning.
Answers
Answer:
1. 1. Because convenient sampling is adopted here data is only gotten from students that eat in the hall in a given period of time so this is a source of bias
Also one study center that is the Hall of only one school is used this is also biased and may affect the result of the study
To avoid this bias a simple random sampling where each student have an equal chance of being selected in the study should be adopted
What is the area of a rectangle
5 inches long and 6 inches wide?
A
29 square inches
B
32 square inches
с
30 square inches
11 square inches
Answers
Answer:
(C) 30 inches
Step-by-step explanation:
The area of a rectangle is always it’s length times its width. Since we are given the length and width, we can multiply these two numbers to get our total area.
[tex]6\cdot5=30[/tex]
Hope this helped!
Answer:
[tex]\large\boxed{Area = 30 inches}[/tex]
[tex]\huge\underline\bold\blue{Given}[/tex]
Length = 5 inches
Breadth= 6 inches
we know that the area of rectangle = length×breadth
Area of rectangle = length × breadth
[tex]\rightarrow[/tex] Area = 5 × 6
[tex]\rightarrow[/tex]Area = 30inches
Hope it helps
a grocery store charges 1.25$ for every 3/4 pound of chocolate purchased. How much will the store charge a customer who purchases 9 pounds of chocolate?
Answers
Given :
A grocery store charges 1.25 $ for every 3/4 pound of chocolate purchased.
To Find :
How much will the store charge a customer who purchases 9 pounds of chocolate .
Solution :
3/4 pound store charges 1.25 $ .
Let , cost of 1 pound is x .
So ,
[tex]\dfrac{3x}{4}=1.25\\\\x=\dfrac{1.25\times 4}{3}\\\\x=1.67\ \$[/tex]
Now , cost of 9 pounds chocolate is :
[tex]C=9\times 1.67\ \$\\\\C=15.03\ \$[/tex]
Therefore , cost of 9 pounds chocolate is 15.03 $ .
Hence , this is the required solution .
Score: 0 of 1 pt
4 of 8 (2 complete)
2.2.15
A large western state consists of 4423 million acres of land. Approximately 19% of this land is federally owned. Find the number of acres that are not federally owned.
Answers
Answer:
3583 million acres
Step-by-step explanation:
If 19% is federally owned, then 81% is not.
0.81 × 4423 million acres = 3583 million acres
that are not federally owned.
_____
This is a typo or refers to some country other than the US. The largest US state (Alaska) is about 425 million acres.
A 1000 L tank now contains 240 L of water. How long will it take to fill the tank using a pump that pumps 25 L per minute
Answers
Answer:
30.4 minutes
Step-by-step explanation:
The tank already has 240L in it, so we need to fill 1000 - 240 = 760L of water.
Since the pump pumps 25L per minute, we can find how many minutes it takes to pump 760L.
760 / 25 = 30.4 minutes.
It will take 30.4 minutes to fill the tank completely.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
Given that, The 1000 L tank contains 240 L of water, therefore, the free space in the tank is :
1000-240
= 760 L
The pump fills the tank at a rate of 25 L per minute.
Therefore, it can be represented as:
25 L = 1 minute
1 L = (1/25) minutes
760 L = (1/25)×760 minutes
760 L = 30.4 minutes.
Hence, it will take 30.4 minutes to fill the tank completely.
Learn more about equations here:
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1) Find an equation of the tangent line at each given point on the curve.x = t2 − 4, y = t2 − 2tat (0, 0)at (−3, −1)at (−3, 3)2) Find the arc length of the curve on the given interval. (Round your answer to three decimal places.)Parametric Equations Intervalx= sqrt1a.gif t y=5t-4 0 ≤ t ≤ 13) Find dy/dx and the slopes of the tangent lines shown on the graph of the polar equation. (If an answer does not exist, enter DNE.)r = 2(1 − sin(θ))
Answers
Answer:
1) at ( 0,0) : y = x/2. at(-3-1) : y = -1. at(-3,3) : y = 2x +9
2) DNE ( does not exist )
Step-by-step explanation:
The general equation of tangent line
y - y1 = m( x - x1 )
attached below is the detailed solution on how i derived the answers above
Which of the following is a rational number
Answers
Joan has $375.24 in a savings
account. She deposits $37.50 each
week and makes no withdrawals.
Which expression represents the
amount of money in the account
in w weeks?
Answers
Answer:
C. 375.24 + 37.50w
Step-by-step explanation:
He already has 375.24
He adds 37.5 every week.
W = the number of weeks.
Example:
=> If he deposits for 10 weeks, then it will be
=> 375.24 + 37.5(10)
=> 375.24 + 375
=> 750.24
The correct expression to represent this problem is Option C.
2x²-y if x=3 and y=8
Answers
Answer:
10
Step-by-step explanation:
2(3)²-8
2(9)-9
18-8=10
Answer:
28
Step-by-step explanation:
Plug in the variable "meaning": (2 × 3)^2 - 82 × 3 = 6Plug 6 in: [tex]6^{2} - 8[/tex] [tex]6^{2}[/tex] = 6 × 6 = 36Plug 36: 36 - 836 - 8 = 28On Saturday morning, Owen earned $26. By the end of the afternoon he had earned a total of $57. Enter an equation, using x as your variable, to determine whether Owen earned $31 or $34 on Saturday afternoon.
Answers
Answer:
$26 + X = $57
$26 + $31 = $57
X = $31
My first time ever answering a question hope it helped =) (And sry it took long)
Step-by-step explanation:
Jacob is the most popular name amongthe 2,086,814 males born in 2000. The Jacobs make up 1.6516% of all males born that year. How many Jacobs were born in 2000?
Answers
Answer:
34,466 children
Step-by-step explanation:
Given the following :
Total number of males born in year 2000= 2,086,814
Percentage number of Jacob's born in year 2000 = 1.6516%
The Jacobs make up 1.6516% of all males born that year?.
The number of Jacob's born in year 2000 will be :
1.6516% of the total number of children born in the year 2000
(1.6516 / 100) × 2,086,814
0.016516 × 2,086,814
= 34465.820024
= about 34,466 children
find the value of x2 values that separate the middle 90% from the rest of the distribution for 8 degrees of freedom
Answers
Answer:
With alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
Step-by-step explanation:
The significance level ∝ = 1- 0.9 = 0.1
But we need the area of the middle so we divide this significance level with 2
so that we get exactly the middle area .
Dividing 0.1/2= 0.05
So we will have two values for chi square
One with 0.9 + 0.05 = 0.95 alpha and one with 0.05 alpha . This is because the chi square is right tailed.
So with alpha 0.95 and 8 degrees of freedom χ²= 2.73
And with alpha 0.05 and 8 degrees of freedom χ²=15.51
This can be shown with a graph.
A cake recipe calls for 2 3/4 cups of sugar. A caterer has 14 1/2 cups of sugar on hand. How many cakes can he make?(answer needs to be rounded down to a whole number)
Answers
Answer:
5 Cakes
Step-by-step explanation:
14.5/2.75=5.27
A cake recipe calls for 2 3/4 cups of sugar. A caterer has 14 1/2 cups of sugar on hand. He can make 5 cakes.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given; A cake recipe calls for 2 3/4 cups of sugar. A caterer has 14 1/2 cups of sugar on hand.
WE have to do 4 x the amount you know you can such as 10.
Then we have to multiply the 1/2 by that same number
Then we divide
14.5/2.75=5.27
Therefore, They can make 5 cakes.
Learn more about the unitary method;
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4(7-13)divided by 3 + (-4) times 2 - (6-2)
Answers
Answer:
[tex]24[/tex]
Step-by-step explanation:
[tex] \frac{4(7 - 13)}{3 + ( - 4)} \times \frac{2 - (6 - 2)}{1} = \frac{28 - 52}{3 - 4} = \frac{ - 24}{ - 1} = 24[/tex]
Hope this helps ;) ❤❤❤
Answer:
24 (Can I have a brainlist, please?)
Step-by-step explanation:
4(7-13)/3 + (-4)2-(6-2)
First we solve the problems in the paraenthesis:
4(7-13)/3 + (-4)2-(6-2)
4(-6)/3 + -4 × 2 -(4)
Now we multiply the ones that are needed to be multiplied:
4(-6)/3 + -4 × 2 -(4)
-24/3 + -8 -(4)
-24/3 + 32
Now we divide:
-24/3 + 32
-8 + 32
And finally we solve the last:
-8 + 32
= 24
Hope that helped!
What’s the difference/same with y/x and y1-y2/x2-x1? Are they both the same?
Answers
They are both similar but not entirely the same.
The first expression y/x means we divide y over x. We divide two values here and we are not subtracting first before division. This expression is useful for when you want to find the variation constant in the equation y = kx (for direct proportion equations).
The other expression (y2-y1)(x2-x1) is where we first subtract the y values, and do the same for the x values, before we divide. This computes the slope of the line through the two points (x1,y1) and (x2,y2). It's also useful to figure out the average rate of change (one application of slope). For problems involving time versus distance, the average rate of change is the average speed in which the object is moving.
Charlie had a -$38.65 balance in his checking account. He deposited $126.00 into the account. What is his new balance?
Answers
Answer: $87.35
Step-by-step explanation:
Answer:
$164.65
Step-by-step explanation:
$38+$126.65=$164.65
is the decimal for 4/3 a repeating decimal? explian
Answers
Answer:
Step-by-step explanation:
Yes, it's a repeating decimal: 1.3333333....
What’s the writing in the form of a/b: -16 *
Answers
Answer:
-16/1
Step-by-step explanation:
-16 in the form a/b can be written as -16/1.
Point q is the image of Q(5, -3) after a translation down 2 units and right 4 units. What are the coordinates of Q?
Answers
Answer:
(9,-5)
Step-by-step explanation:
When you go down, the number will decrease. The vertical position is the Y axis. -3-2=5.
When you go right, the number will increase. The horizontal position is the X axis. 5+4=9
(9,-5)
Hope this helps :-)
8 The health department of the city wants to evaluate the increase in respiratory illnesses among citizens over the past 15 years. Which meas would be displayed in a graph most appropriately representing this information? OA. the percent of Increase of all illnesses per year OB. the total increase of all illnesses per year the percent of increase in the number of hospitals per year D. the percent of increase of respiratory illnesses per year Reset Next Reserved
Answers
Answer:
Option D : "he percent of increase of respiratory illnesses per year"
Step-by-step explanation:
Since you want to show how the respiratory illnesses increase over the last 15 years, then plot a graph that shows such increase year by year.
Find the median for the given set of data.
5/8, 3/4, 1&1/8, 1&1/4
A. 15/16
B. 7/8
C. 13/16
Answers
For each point find the coordinates of the image point under a half turn about the origin
a(3,0)
b(3,4)
c(-1,-4)
d(r,s)
Answers
Answer:
see explanation
Step-by-step explanation:
Under a half turn about the origin
a point (x, y ) → (- x, - y ) , thus
(3, 0 ) → (- 3, 0 )
(3, 4 ) → (- 3, - 4 )
(- 1, - 4 ) → (1, 4 )
(r, s ) → (- r, - s )
The coordinates of the image point under a half-turn about the origin(3, 0 ) is (- 3, 0 ), (3, 4 ) is (- 3, - 4 ), (- 1, - 4 ) is (1, 4 ), (r, s ) is (- r, - s ).
What is a mirror image of a point in coordinate geometry?The mirror image of a point in coordinate geometry is the image formed with respect to the x-axis, y-axis, or origin.
A point (x, y ) has image point (- x, - y )
Thus,
The coordinates of the image point under a half-turn about the origin(3, 0 ) is (- 3, 0 )
The coordinates of the image point under a half-turn about the origin(3, 4 ) is (- 3, - 4 )
The coordinates of the image point under a half-turn about the origin(- 1, - 4 ) is (1, 4 )
The coordinates of the image point under a half-turn about the origin(r, s ) is (- r, - s )
Learn more about images;
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Neal is a coffee drinker. At the local coffee shop, the price
of a cup of coffee is $3. Neal's total benefits from
drinking coffee are indicated in the accompanying table.
Use this information to calculate Neal's marginal benefit
of consuming each cup of coffee.
Quantity of
coffee
(cups per day)
Total
benefits
2
3
$8
$14
SI8
$20
$21
4
5
a. The marginal benefit of the first cup is 5
b. The marginal benefit of the second cup is $
10
c. The marginal benefit of the third cup is $15
d. The marginal benefit of the fourth cup is 25
e. The marginal benefit of the fifth cup is s
f. Neil should consume
cups of coffee per day.
Answers
Answer and Step-by-step explanation: Marginal Benefit is the maximum a person is willing to pay for an additional good or service. It can be calculated as:
[tex]marginal=\frac{Change total benefit}{Change quantity}[/tex]
For each cup of coffee:
For the first cup, benefit is $8;
For the second:
[tex]marginal=\frac{14-8}{2-1}[/tex]
marginal = 6
For the third:
[tex]marginal=\frac{18-14}{3-2}[/tex]
marginal = 4
For the fourth:
[tex]marginal=\frac{20-18}{4-3}[/tex]
marginal = 2
For the fifth:
[tex]marginal=\frac{21-20}{5-4}[/tex]
marginal = 1
The cost of the coffe is $3, so comparing benefit and cost, Neal should consume 4 cups of cofee per day.
for the equation f(x)=x^2-4x+1
f(x+h)-f(x)/h = ?
Answers
Answer: f(x)=x2-4x
Step-by-step explanation: