Answer:
0.3472 = 34.72% probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.02.
Step-by-step explanation:
To solve this question, we use the normal probability distribution and the central limit theorem.
Normal probability distribution:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem:
The Central Limit Theorem estabilishes 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.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
Proportion [tex]p = 0.2[/tex], sample of [tex]n = 81[/tex]. So
[tex]\mu = p = 0.2[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.2*0.8}{81}} = 0.0444[/tex]
Approximate the probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.02.
Probability of the sampled proportion being between 0.2 - 0.02 = 0.18 and 0.2 + 0.02 = 0.22, which is the pvalue of Z when X = 0.22 subtracted by the pvalue of Z when X = 0.18. So
X = 0.22
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.22 - 0.2}{0.044}[/tex]
[tex]Z = 0.45[/tex]
[tex]Z = 0.45[/tex] has a pvalue of 0.6736
X = 0.18
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.18 - 0.2}{0.044}[/tex]
[tex]Z = -0.45[/tex]
[tex]Z = -0.45[/tex] has a pvalue of 0.3264
0.6736 - 0.3264 = 0.3472 = 34.72% probability that the sampled fraction of voters favoring the bond issue will not differ from the true fraction by more than 0.02.
Brad owns a successful corporation that has a substantial earnings and profits. During the year, the following payments were made by corporation
Answer:
That's great for Brad, wait are you talking about the Brad from clash royale? if so im impressed
Step-by-step explanation:
(k+7)2=289
Set1
Set2
Answer:
Two solutions were found :
1. k = 10
2. k = -24
step by step explaination : you dont need to know the step by step explaination anyways hope it helps
A baker’s dozen has 13 muffins. Serena ordered 30 baker’s dozens. How many muffins did Serena order?
Planes A and B intersect.
Vertical plane B intersects horizontal plane A. Point W is on the line where the planes intersect. Vertical line m is on the left half of plane A. Horizontal line n intersects line m at point X and line k at point W. Line l is on the lower half of plane B with point Y.
Which describes the intersection of plane A and line m?
line k
line n
point X
point W
Answer:
Point x
Step-by-step explanation:
got it right on edge 2021
Answer:
c
Step-by-step explanation:
Pls help I’ll brainlest due today
Answer:
9/8 I think
Step-by-step explanation:
The system of equations y=-2x+3 and y=x is graohed. What is the solution to the system of equations
Answer:
The solution to this system of equations is y = 1, x = 1
Step-by-step explanation:
We know that...
(1) y = - 2x + 3
(2) y = x
Then we just substitute the value of x that we are given in equation (2).
And so we get....
y = -2x + 3
x = - 2x + 3
3x = 3
x = 1
From equation (2) we know that y = x, so since x equals 1 y is also 1. There for the solution to this system of equations is (1,1)
which ratio is equivalent to 8/6 3/24/24/32/32/24/24/3
Answer:
32:24
Step-by-step explanation:
Answer:
32/24
Step-by-step explanation:
(-0.25х -8) - (1.5х + 6.4) plz
Answer:
Step-by-step explanation:
-0.25x-8-1.5x-6.4=-1.75x-14.4
Cheryl is buying lace for her dance costume. One foot of lace costs 3 dollars. How much does each amount cost?
3/4 of a foot?
Answer:
3/4 of a foot will cost $2.25.
Step-by-step explanation:
This question is solved by rule of three, due to proportions.
One foot of lace costs 3 dollars. How much is 3/4 of a foot going to cost?
1 foot - 3 dollars
3/4 foot - x dollars
[tex]x = 3 \times \frac{3}{4} = \frac{9}{4} = 2.25[/tex]
So
3/4 of a foot will cost $2.25.
write the equation of a line with the given two points in slope intercept form.
(5,1) (-3,2)
PLZ HELP!
Answer:
y = -⅛x + 1⅝
Step-by-step explanation:
HELP PLEASE ITS DUE!!!! PLEASE I NEED HELPPPPPPP
Pe nu cerc de central O se considera punctul ABC astfel incat punctele A B C sunt coliniare .Care este masura unghiului ACB
Which of the following expressions has a coefficient of 10 and a constant of 5
A) 10x + 5
B) 10 + 5x
C) 10 + 5
D) 10 + 5
-- someone already answered this.
answer:
10x + 5
credits: https://brainly.com/question/17673900
Solve the system by substitution.
-5x + 3y = 2
y = 2x
Answer:
Step-by-step explanation:
-5x +3(2x) = 2
-5x +6x = 2
x=2
23. The density of mercury is 13g/cm cubed. If there are 4 cm cubed of mercury, what is the mass?
A. 3.25 g
B.0.31 g
C. 52 g
D. 39 g
Answer:
B
Step-by-step explanation:
Strawberries are $3.99 per pound. If a customer bought $30 worth, how many pounds did he buy? $
Blank 1:
Answer:
7.5
Step-by-step explanation:
Divide 30 by 3.99
30/3.99=7.5Calculate the volume, in cubic centimeters, of a box which is 125 cm long, 37 cm wide, and 68 cm high. Report your answer with correct significant figures in cubic centimeters.
Answer:
[tex]Volume = 314500cm^3[/tex]
Step-by-step explanation:
Given
[tex]Length = 125cm[/tex]
[tex]Width = 37cm[/tex]
[tex]Height = 68cm[/tex]
Required
Determine the volume
Volume is calculated as:
[tex]Volume = Length * Width * Height[/tex]
Substitute values for Length, Width and Height
[tex]Volume = 125cm * 37cm * 68cm[/tex]
[tex]Volume = 314500cm^3[/tex]
Hence, the volume of the box is [tex]314500cm^3[/tex]
What is the distance between the points (-4, 2) and (3, -5)?
Answer:
c
Step-by-step explanation:
the other guy is bad
what is (t - 7 )3? ive tried it many times and i cant get it. Thanks !
Answer:
3t-21 hope I helped you! >w<
You have a coupon for 30% off your dinner. Your total bill was $50. You also need to pay a 7% sales tax and leave a 22% tip. With the discount, tip + tax included, how much was your dinner? I am having trouble with this one
6) Steven receives $5.75 per hour and 3% commission on sales. One week he worked 40 hours and sold $2,500
worth of goods. How much did he earn that week?
Answer:
$230 for the hourly pay of 5.75×40 and $75 for the 2500x3% so total pay is $305.
Explain how to round 74.685 to the nearest hundredth
Answer:
the answer will be 74.700
Step-by-step explanation:
Determine whether the relation is or is not a function.
Answer:
Not a function because it does not pass the Vertical Line Test.
{35, 42, 49, 56, ...} finite or infinite?
Answer:
infinite
Step-by-step explanation:
What is the solution to the system of equations below?
X+ 3y = 15 and 4x+2y= 30
O (6,3)
O (3,6).
O (7,-6)
O (-6, 7)
Answer:
6,3
Step-by-step explanation:
given equtions are
x+3y=15______(1)
4x+2y=30______(2)
multiplying (1) by 4
on solving, 4x+12y=60_____(3)
substracting eqution (3) and (2)
4x+12y-(4x+2y)=60-30
⇒10y=30
on solving,
y=3
substituting the value of y in equation (1)
x+3(3)=15
on solving,
x=6
Answer:
A
Step-by-step explanation:
(6,3)
how to find the slope
Answer:
im thinking its c
just do rise over run
count the y values from bothe points then the x then put it as a fraction y/x
Step-by-step explanation:
the ratio of boys to girls in a class is3:2 there are 25 students in this class how many are girls how many are boys.
Answer:
Out of 25, the number of girls to boys is 15/10, which is equivalent to 3/2.
Step-by-step explanation:
Marianna just completed her findings in her investigation of the importance
of sunlight in the growth of plants. She has to submit a report of no less than
4,900 words in 15 pages. She can only use two types of font for her report.
The normal font size allows 300 words per page while the smaller italic font
allows 350 words per page. What is the maximum number of pages in her
report that can be set using the normal font size?
Please I need help!!!!!
Answer:
17 pages
Step-by-step explanation:
if not that then 15 since it says "less than 4,900 words in 15 pages"
Write the slope-intercept form of the equation of the line.
Please someone help me!!
Answer:
y=-2x+2
Step-by-step explanation:
ummmmm can someone help me on this :)