A bank manager wants to know the mean amount of mortgage paid per month by homeowners in an area. A random sample of homeowners selected from this area showed that they pay an average of per month for their mortgages. The population standard deviation of such mortgages is . a. Find a confidence interval for the mean amount of mortgage paid per month by all homeowners in this area. Round your answers to two decimal places. 1538.51 to 1627.49 dollars b. Suppose the confidence interval obtained in part a is too wide. Select all of the ways the width of this interval can be reduced.
Answers
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
The 97% confidence interval is [tex]1528 < \mu < 1612 [/tex]
b
Option A and Option D are correct
Step-by-step explanation:
From the question we are told that
The sample size is n = 119
The sample mean is [tex]\$ 1570[/tex]
The population standard deviation is [tex]\sigma = \$ 211[/tex]
Generally given that the confidence level is 97% then the level of significance is mathematically represented as
[tex]\alpha = (100 - 97 )\%[/tex]
=> [tex]\alpha = 0.03[/tex]
From the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.17[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
[tex]E = 2.17* \frac{211}{\sqrt{ 119 } }[/tex]
=> [tex]E = 41.98 [/tex]
Generally the 97% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]1570 - 41.98 < \mu < 1570 + 41.98 [/tex]
=> [tex]1528 < \mu < 1612 [/tex]
Generally looking at confidence interval we see that the width is dependent on the size of the margin of error.
Generally the margin error is directly proportional to the critical value of [tex]\frac{\alpha }{2}[/tex] which increases when the confidence level increases and vise versa
Also the margin error is inversely proportional to the square root of sample size
Hence to reduce the width of the confidence interval we need to lower the confidence level and increase the sample size
Related Questions
A farmer watered 3/7 of a field. What percentage is equivalent to the fraction of the field the farmer watered?
Answers
Answer:510
Step-by-step explanation:
Answer:
510
Step-by-step explanation:
Write the sentence as an inequality.
A number is less than 6 and greater than 2
Answers
Answer:
6 > x > 2
Step-by-step explanation:
This could be wrong, but if the number is less than six, and greater than two, itd look like that!
Steve is buying apples for the fifth grade. Each bag holds 12 apples. If there are 68 students total, how
many bags of apples will Steve need to buy if he wants to give one apple to each student?
Steve will need to buy
bags.
Answers
Answer:
mark me brainlest
Step-by-step explanation:
7
packets
Explanation:
Steve needs to know how many groups of 12 there are in the 75 students.
75
÷
12
=
6
1
4
However, Steve can only buy full packets of 12.
He needs 7 packets of apples.
I he only buys 6, there will not be enough for all the 5th Graders.
The diagram below represents the side view of a bike ramp.
Which of the following is closest to the value of x ?
Answers
Answer:
32
Step-by-step explanation:
We are finding X and it connects to the base and the height, so it is going upward only a bit, so you add the base to the height or 26 + 6 = 32.
Answer:
32
Step-by-step explanation:
All you need to do is add 26 + 6=32
Help me please ASAP Is the function y=5/4 linear and nonlinear
Answers
Answer:
linear
Step-by-step explanation:
Let X be an exponential random variable with parameter λ=2 . Find the values of the following. Use 'e' for the base of the natural logarithm (e.g., enter e^(-3) for e−3 ).
a) E[(3X+1)2]=
b) P(1≤X≤2)=
Answers
Answer:
a
[tex]E[(3X+1)^2]= 8.5 [/tex]
b
[tex]P(1 < X < 2)=0.1170 [/tex]
Step-by-step explanation:
From the question we are told that
The parameter of X is [tex]\lambda = 2[/tex]
Generally the expected value of X is
[tex]E(X) = \frac{1}{\lambda }[/tex]
[tex]E(X) = \frac{1}{2}[/tex]
=> [tex]E(X) = 0.50 [/tex]
Generally we have that
[tex]E(X^2) = E(X)^2 + E(X)^2[/tex]
=> [tex]E(X^2) = [\frac{1}{2}] ^2 + [\frac{1}{2} ]^2[/tex]
=> [tex]E(X^2) = 0.5 [/tex]
Generally
[tex]E[(3X+1)^2]= E(9x^2 + 1 + 6x)[/tex]
=> [tex]E[(3X+1)^2]= 9E[X^2] + 1 + 6 E[X])[/tex]
=> [tex]E[(3X+1)^2]= 9* 0.5 + 1 + 6 * 0.5 [/tex]
=> [tex]E[(3X+1)^2]= 8.5 [/tex]
Generally
[tex]P(1 < X < 2)= P(X < 2) - P(X < 1)[/tex]
Here [tex]P(X < 2 ) = e^{- 2 * \lambda }[/tex]
=> [tex]P(X < 2 ) = e^{- 2 * 2 }[/tex]
=> [tex]P(X < 2 ) = e^{- 4}[/tex]
and
[tex]P(X < 1 ) = e^{- 1 * \lambda }[/tex]
[tex]P(X < 1 ) = e^{- 1 * 2 }[/tex]
[tex]P(X < 1 ) = e^{-2 }[/tex]
So
[tex]P(1 < X < 2)= e^{-2 } - e^{- 4} [/tex]
[tex]P(1 < X < 2)=0.1170 [/tex]
Is so easy pls help 20 points
Answers
Answer:
24
Step-by-step explanation:
bc 60-36=24 (idk if this is right)
yavonee reads 14 pages in 28 mins, at this rate, how many pages does she read in 50 mins
Answers
Answer:
yavonee can read 25 pages in 50 minutes with the same rate.
Step-by-step explanation:
calcuate how may pages does yavonee read in 1 minute
14/28
= 1/2 or 0.5
0.5 * 50
= 25
In 50 minutes Yavonee can read 100 pages with a unit rate of 2 pages per minute.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Yavonee reads 14 pages in 28 mins.
∴ In 1 minute she reads (28/14) = 2 pages.
So, In 50 minutes she can read (2×50) = 100 pages.
learn more about the unitary method here :
https://brainly.com/question/28276953
#SPJ5
Suppose you have a total of $2.25 in dimes and
nickels. You have twice as many dimes, as nickels.
Which system of equations could be used to
determine how many of each coin you have?
Answers
Answer:
n = number of nickels
2n = number of dimes
n($0.05) + 2n($0.10) = $2.25
0.05n + 0.2n = 2.25
0.25n = 2.25
n = 2.25/0.25 = 9
2n = 2(9) = 18
You has 9 nickels and 18 dimes
Step-by-step explanation:
urgent will mark brainliest
which answers are elements of the solution set of the inequality? check all answers that apply. x-46>/-79
A. -39
B. -45
C. -33
D. 25
E. 14
F. -25
Answers
First, isolate the variable:
x>-33
The answers would be 25, 14, -25.
I am not sure if that is a more than sign or a more than or equals sign; if it is a more than sign the answers mentioned above are the only answers, but if it a more than or equals sign, the answers are 25, 14, -25, -33.
If it helped please consider giving be brainliest :)
Answer:
C, D, E, FStep-by-step explanation:
Solving in steps
x - 46 ≥ - 79x ≥ 46 - 79x ≥ -33Correct answer choices:
C. -33 D. 25E. 14F - 25Select the correct answer.
In a figure, a pair of parallel lines is cut by a transversal. What is the measure of angle C if the measure of angle B is 35°?
Answers
Answer:
145 . this is because angles on a straight line add up to 180 degrees
Answer:
c.145
Step-by-step explanation:
Reese loves to drink healthy green smoothies. A 16oz serving of smoothie has 170 calories. How many calories are in a 24oz smoothie?
Answers
Answer:
255 calories.
Step-by-step explanation:
There are many different ways to solve this, but I only know two.
First I noticed that 16 and 24 were both divisible by 4 so divided 16 by 4 and got 4. Then I divided 170 by 4 and got 42.5. So then I divided 24 by 4 and got 6. I multiplied 6 by 255.
OR
Divide 170 by 16 which gave me 10.625 which is the unit rate or constant of proportionality. So I multiplied 10.625 by 24 and got 255.
Please answer I need help badly
Answers
The cast of the play had a party. The drama teacher served 20 cookies and 40 carrot sticks as refreshments. Each cast member ate the same number of whole cookies and the same number of carrot sticks. Nothing was leftover. The drama teacher did not eat. How many cast members must have been at the party?
Answers
Answer:
20 cast members
Step-by-step explanation:
Each cast member must've ate 1 cookie and 2 carrot sticks.
Nicholas took a total of 10 quizzes over the course of 2 weeks. How many weeks of school will nicholas have attend this quarter before he will have taken a total of 15 quizzes?
Answers
Answer:
would be 3 weeks
Step-by-step explanation:
He is taking about 5 each week he has done 10 in 2 weeks so should be 3 weeks.
Answer:
3 weeks
Step-by-step explanation:
2 weeks is 10 quizzes and 1 week is 5 quizzes, so 2+1=3
What number is an interger?
Answers
Answer:
21, 4, 0, and −2048 are intergers
Step-by-step explanation:
Using the equation below, determine the range for the given domain values.
y= x 4 ; D={-4, 2, 8}
Answers
If it is :
[tex]y = f(x) = {x}^{4} [/tex]
_________________________________
[tex]f( - 4) = ({ - 4})^{4} = 256 [/tex]
_________________________________
[tex]f(2) = {2}^{4} = 16 [/tex]
_________________________________
[tex]f(8) = {8}^{4} = 4096 [/tex]
Range = { 16 , 256 , 4096 }
##############################
If it is :
[tex]y = f(x) = 4x[/tex]
_________________________________
[tex]f( - 4) = 4( - 4) = - 16[/tex]
_________________________________
[tex]f(2) = 4(2) = 8[/tex]
_________________________________
[tex]f(8) = 4(8) = 32[/tex]
Range = { -16 , 8 , 32 }
##############################
And we're done.....♥️♥️♥️♥️♥️
Assume that a procedure yields a binomial distribution with a trial repeated
n=5 times. Use some form of technology to find the probability distribution given the probability p=0.156 of success on a single trial.
Answers
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ qⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1−p).
n = 5, p = 0.156, and q = 0.844.
r = 0, P = ₅C₀ (0.156)⁰ (0.844)⁵⁻⁰ = 0.428
r = 1, P = ₅C₁ (0.156)¹ (0.844)⁵⁻¹ = 0.396
r = 2, P = ₅C₂ (0.156)² (0.844)⁵⁻² = 0.146
r = 3, P = ₅C₃ (0.156)³ (0.844)⁵⁻³ = 0.027
r = 4, P = ₅C₄ (0.156)⁴ (0.844)⁵⁻⁴ = 0.002
r = 5, P = ₅C₅ (0.156)⁵ (0.844)⁵⁻⁵ ≈ 0
will mark brainliest, a THX, friend request, and will rate ur answer
Answers
Answer:
35/4
Step-by-step explanation:
8 × 4 = 3232 + 3 = 35Write 35 over the original denominator: 35/4I hope this helps!
Help ASAP!!!!
A company sells herb blends for cooking. The tables below show the number of teaspoons for each herb in each blend and the cost for each blend.
What is the cost of basil per teaspoon?
o $0.15
o $0.18
o $0.19
o $0.23
Answers
Answer:
$0.23 or D
Step-by-step explanation:
Edg :)
The cost of one teaspoon of basil is $0.23. Therefore, option D is the correct answer.
We need to find the cost of basil per teaspoon.
How to interpret the data table?Interpretation of the data table is as follows:
Identify the subject under study.Identify the variable(s) presented in the table.Identify the measuring unit used (frequencies, percentages, rates, etc.)Read the information presented in table cells.Let the cost of one teaspoon of basil be $x, oregano be $y and parsley be $z.
Now, x+2y+3z=1.06-----(1), x+y+2z=0.72-----(2) and 2x+2y+z=0.99-----(3)
Equation (1)-(2), we get
x+2y+3z-(x+y+2z)=1.06-0.72
⇒y+z=0.34-----(4)
⇒z=0.34-y
Substitute z=0.34-y in equation (3).
That is, 2x+2y+0.34-y=0.99
⇒2x+y+0.34=0.99
⇒2x+y=0.65---(5)
Substitute z=0.34-y in equation (2)
Equation (5)-(4), we get
x+y+2(0.34-y)=0.72
⇒x+y+0.68-2y=0.72
⇒x-y=0.04-----(6)
Add equations (5) and (6), and we get
2x+y+x-y=0.65+0.04
⇒3x=0.69
⇒x=0.23
Therefore, the cost of basil per teaspoon is $0.23.
To learn more about the system of equations visit:
https://brainly.com/question/9351049.
#SPJ5
f(3) = 5x + 3. Find the inverse of f(x).
O A. f-'(x) =
B. -1 (2) = 3 – 52
O c. f-'(x) =
OD. f-1(x) = 5x – 3
Answers
PLEASE HELP!! Find the market equilibrium point for the following demand and supply equations
Answers
9514 1404 393
Answer:
(p, q) = (16, 20)
Step-by-step explanation:
You can add the two equations together to make one from which q can be eliminated:
(4p) +(3p -q) = (-q +84) +(28)
7p -q = -q +112 . . . . simplify
7p = 112 . . . . . . . . . . add q
p = 112/7 = 16
Using this value in the second equation, we get ...
3·16 -q = 28
48 -28 = q = 20 . . . . . add q-28
The equilibrium point is (p, q) = (16, 20).
Antonio, que tiene 64 lápices, tiene el doble de lápices que Lucía;
Lucía tiene el doble que Carlos y Carlos tiene el doble que Diana.
Answers
Answer:
lucia tiene 32
carlos tiene 16 y
diana tiene 8
How to get x by its self y=Mx+c
Answers
Answer:
Subtract c, then divide by m.
Solve for h.
2h − 1 = 1
h =
Answers
Answer:
h = 1
Step-by-step explanation:
2h - 1 = 1
2h - 1 + 1 = 1 + 1
2h = 2
2h/2 = 2/2
h = 1
Check:
2(1) - 1 = 1
2 - 1 = 1
1 = 1
Answer:
h = 1
Step-by-step explanation:
Add 1 to each side, so it now looks like this: 2h = 2Divide each side by 2 to cancel out the 2 next to h. It should now look like this: h = 1I hope this helps!
What value of x makes this equation true 5(x-3)=20
Answers
Answer:
X=7
Step-by-step explanation:
5x - 15 =20
5x=15+30
5x=35
Divide by 5
X=7
Add using the number line. −11+5 Drag and drop the word SUM to the correct value on the number line.
Answers
Answer:
-6
Step-by-step explanation:
Answer:
-6
Step-by-step explanation:
did the test
Marcus is buying a pair of running shoes that are discounted 20% from the original price
of $100. The store is also having a holiday sale, so they will take an additional 20% off the
sale price. How much will Marcus pay for his shoes?
Answers
Answer: $64
Step-by-step explanation:
20% of 100 is 20 so 100-20=80. Also 20% of 80 is 16. So 80-16=64. So that’s the answer.
please answer!!
Graphs of Linear Functions
write an equation for a line parallel to y= 2x- 4 and passing through the point (2,7)
y= ?
Answers
Answer:
Y= -8
Step-by-step explanation:
i think so......
KKKKKKKKKKKKKKKKKKK
help anyone please??
Answers
Answer:
1.
Collinear points mean they are on the same line. That leaves us with answer d. F, E, G
2.
In this case, the intersection of the 2 planes is a line. 2 points both planes contain are B and C, so the intersection can be named as answer b: Line BC
3.
2 points define a line, so therefore the answer to the question is answer b. 1
Hoped this helped. If it did, could you please consider giving me a brainliest? :)