Answer:
The sample proportion of size 177 is more likely to exceed 22%.
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 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]
Suppose both populations of hellbenders are known to have ranavirus infections at a rate of 25%.
This means that [tex]\mu = p = 0.25[/tex]
Sample of size 118:
[tex]n = 118, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0399[/tex]
Probability of sample proportion above 22%.
This is 1 subtracted by the pvalue of Z when X = 0.22. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.22 - 0.25}{0.0399}[/tex]
[tex]Z = -0.75[/tex]
[tex]Z = -0.75[/tex] has a pvalue of 0.2266
1 - 0.2266 = 0.7734
0.7734% probability that a random sample of size 118 exceeds 22%.
Sample of size 177:
[tex]n = 177, so [tex]s = \sqrt{\frac{0.25*0.75}{118}} = 0.0325[/tex]
Probability of sample proportion above 22%.
This is 1 subtracted by the pvalue of Z when X = 0.22. So
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.22 - 0.25}{0.0325}[/tex]
[tex]Z = -0.92[/tex]
[tex]Z = -0.92[/tex] has a pvalue of 0.1788
1 - 0.1788 = 0.8212
0.8212 = 82.12% probability that a random sample of size 177 exceeds 22%.
82.12% > 77.34%, so the sample proportion of size 177 is more likely to exceed 22%.
The sample proportion that is more likely to exceed 22% is; the sample proportion with a sample size of 177
Central Limit Theorem
We are given;
Population proportion; p = 25% = 0.25
Now, in central limit theorem, the formula for standard deviation is;
σ = √(p(1 - p)/n)
For a sample size of 118, we have;
σ = √(0.25(1 - 0.25)/118)
σ = √0.001588983
σ = 0.03986
Similarly, for a sample size of 177, we have;
σ = √(0.25(1 - 0.25)/177)
σ = √0.001059322
σ = 0.032547
Since we want to find which of the two sample proportions will likely exceed 22% which is p₀ = 0.2, we will use the formula;
z = (p₀ - p)/σ
For sample size of 118, we have;
z = (0.22 - 0.25)/0.03986
z = -0.75
From online p-value from z-score calculator, we have;
p-value = 0.7734 or 77.34%
For sample size of 177, we have;
z = (0.22 - 0.25)/0.032547
z = -0.92
From online p-value from z-score calculator, we have;
p-value = 0.8212 or 82.12%
The p-value of the sample of 177 is higher than the p-value for the sample of 118 and so we can say that the sample proportion with a sample size of 177 is more likely to exceed 22%
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is 0.12 greater than 0.9?
Solve for x
(19x-18)
(7x+1)
(10x-9)
Answer:
Step-by-step explanation:
Exterior angle property: Exterior angles equals the sum of remote angles
19x - 18 = 7x + 1 + 10x - 9
19x - 18 = 7x + 10x + 1 - 9 {Combine like terms}
19x - 18 = 17x - 8 {Subtract 17x from both sides}
19x - 17x - 18 = -8
2x - 18 = -8 {Add 18 to both sides}
2x = -8 + 18
2x = 10
x = 10/2
x = 5
What is the volume of this figure?
11 cm
8 cm
6 cm
10 cm
Answer:
use mathwa.y it will help
Step-by-step explanation:
Some equilateral triangles are not isosceles.
O A. True
O B. False
ANSWER
THE ANSWER IS FALSE
Step-by-step explanation:
false
(x2−4x+9)−(3x2−6x−7)
Answer:
wrong question..
please set your question
What is 7 written as a percent? A. 7.2% B. 27% C. 72% D. 720%
Which one of the following statements is FALSE?
A
sin 70' = cos 20
B sin 15° = cos 65
С
COS 43 = sin 47
D
sin 12 = cos 78
Answer:
D because you have to cos
Answer:
B and D
Step-by-step explanation:
sin(15)=0.25
cos(65)=0.42
Jorge walked 21/3 miles. Samuel walked 1/4 of the distant that Jorge walked how far did Samuel walk
Easton is driving to a concert and needs to pay for parking. There is an
automatic fee of $8 just to enter the parking lot, and when he leaves the lot,
he will have to pay an additional $3 for every hour he had his car in the lot.
How much total money would Easton have to pay for parking if he left his car
in the lot for 2 hours? How much would Easton have to pay if he left his car in
the lot for t hours?
Answer:
If he left the car in the lot for 2 hours, he would have to pay 14 dollars. if he left it for "t" hours, he would have to pay 11 + 3t dollars
Step-by-step explanation:
Think of it like this: "a" represents the total amount of money Easton will spend, t represents time in hours. $11 + $3*t = a
The length of time, in hours, it takes a train to travel to city B varies inversely with the train’s speed. The train Carole is traveling on is moving at a speed of 70 miles per hour, and it takes her 4 hours to arrive. If the train Steve is traveling on is moving at a speed of 50 mph, how long will it take him to arrive at City B?
Answer:
Step-by-step explanation:
4 h × (70 mi)/h = 280 mi
280 mi × (1 h)/(50 mi) = 5.6 h
The time taken by him to arrive at City B will be 5.6 hours.
What are ratio and proportion?A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.
The time span, in hours, it takes a train to go to city B fluctuates contrarily with the train's speed.
V x T = Constant
The train Carole is going on is moving at a speed of 70 miles each hour, and it requires her 4 hours to show up. In the event that the train, Steve is going on, is moving at a speed of 50 mph.
Let 't' be the time. Then the equation is given as,
t x 50 = 4 x 70
50t = 280
t = 280 / 50
t = 28 / 5
t = 5.6 hours
The time taken by him to arrive at City B will be 5.6 hours.
More about the ratio and the proportion link is given below.
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if 6 student share 1/2 pounds of modeling clay equally ,how much claydose each student get
Answer:
C. 1/12 poundStep-by-step explanation:
Divide 1/2 by 6 to find each student's share:
1/2:6 = 1/12 of a poundCorrect choice is C
PLEASE HELP!!!! What is the slope of the line that passes through the points (2, 3) and (6, 8)
Answer:
[tex]\frac{5}{4}[/tex]
Step-by-step explanation:
to find the slope (m) of a line:
[tex]m= \frac{y_2 - y_1}{x_2 - x_1}[/tex]
where y₁ = 3
y₂ = 8
x₁ = 2
x₂ = 6
plug into the equation:
[tex]m = \frac{8 - 3}{6 - 2} \\m = \frac{5}{4}[/tex]
so the slope is [tex]\frac{5}{4}[/tex]
Rahul made three Indian clay curry pots. He wants to see if he
can place them in the oven at the same time.
The diameter of the second pot is of the diameter of his first
pot.
cm wider than the diameter
The diameter of the third pot is
of his second pot.
The sum of the diameters of the three pots is 47.5 cm.
What equation represents the sum of the diameters of all three lord and what is the value of y?
Answer:2.234
Step-by-step explanation:
44 is 11% of what number?
Answer:
400
Step-by-step explanation:
look it up. it says 400.
The required number is 400 for which 44 is 11%.
The percentage is a way to express a proportion or a fraction as a fraction of 100. It is commonly used to compare values or quantities relative to a whole or a total.
To calculate a percentage, you typically divide a part or a quantity by the whole or the total and then multiply the result by 100. The resulting value represents the percentage equivalent of the part or quantity.
It implies that a percentage value represents a certain number out of 100 parts.
Given that 44 is 11% of the number. The unknown number is calculated as,
x (11%) = 44
[tex]x \times \dfrac{11}{100} = 44\\x = \dfrac{44\times100}{11}\\x=400[/tex]
Therefore, the number is 400.
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Right Triangle ABC has its right angle at C, BC = 4, and AC= 8.
What is the value of the trigonometric ratio?
cos B
csc B
tan A
Drag a value to each box to match the trigonometric ratio?
9514 1404 393
Answer:
cos B = (√5)/5
csc B = (√5)/2
tan A = 1/2
Step-by-step explanation:
The length of hypotenuse AB is given by the Pythagorean theorem:
AB² = AC² +BC²
AB² = 8² +4² = 64 +16 = 80
AB = √80 = 4√5
The mnemonic SOH CAH TOA can help you remember the needed ratios.
Cos = Adjacent/Hypotenuse
cos B = BC/AB = 4/(4√5)
cos B = (√5)/5
__
Sin = Opposite/Hypotenuse
csc = 1/sin = Hypotenuse/Opposite
csc B = AB/AC = (4√5)/8
csc B = (√5)/2
__
Tan = Opposite/Adjacent
tan A = BC/AC = 4/8
tan A = 1/2
Answer:
tan A = 1/2
cos B = √5/5
csc B = √5/2
Step-by-step explanation: I took the test
. Which expression represents the phrase below? 4 less than the product of 8 and a number, x *
A. 8 - 7x
B. (8 + 4) - 3
C. 4 - 8x
D. 8x - 4
Answer:
8x-4
Step-by-step explanation:
4 is less meaning it is subtraction and product of 8 and x is 8x
5
Which equation will solve the following word problem? The professor has 390 books that he wants to display in his office. Each shelf can hold 65 books. How many shelves will he need?
390s = 65
390(65) = s
s/390 = 65
390 = 65s
Answer:
6 shelves
Step-by-step explanation:
Let the number of shelves needed be s
If the total number of books to be displayed is 390books
If Each shelf can hold 65 books, then;
1 shelf = 65books
To know the total shelf needed;
s = 390 books
Divide both expressions
1/s = 65/390
65s = 390
Divide through by 65
65s/65 = 390/65
s = 390/65
s = 6
Hence 6 shelves will be needed
For what value of x is JKLM a parallelogram? Marking people as brainlist
9514 1404 393
Answer:
C 21
Step-by-step explanation:
You can approach this any of several ways. The following conditions must be true:
adjacent angles total 180°
opposite angles are congruent
Using the latter relation on the upper right and lower left angles, we have ...
4x -1 = 3x +20
x = 21 . . . . . . . . . . add 1-3x to both sides
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is five times the measure of the first angle. The third angle is 22 more than the second. Let x, y, and z represent the measures of the first second, and third angles, respectively. Find the measures of the three angles.
Answer:
x=30°, y=64°, z=86°
Step-by-step explanation:
Make a system of equations using the information given.
x + y + z = 180 <-- from "the sum of interior angles equals 180 degrees"
y + z = 5x <-- from "sum second angle and third angles is five times the first angle"
z = y + 22 <-- from "the third angle is 22 more than the second"
Eliminating the x variable to makes the equations easier to solve.
5x + 5y + 5z = 900
-(5x = z + y)
= 5y + 5z = 900 - z - y
= 6y + 6z = 900
= y + z = 150
Now substitute z for (y+22)
y + (y + 22) = 150
2y + 22 = 150
2y = 128
y = 64
Now find z when y=64
z = (64) + 22
z = 86
Finally, plug in z and y into one of the equations with x and evaluate for x.
x + 64 + 86 = 180
x + 150 = 180
x = 30
What is the answer to “Animal Cells Are More Interesting Than Plant Cells.”
Answer:
This is more of a question that involves opinion, I prefer to studdy animal cells but that is merely my opinion. Plant cells are interesting too and may be more interesting to someone else, But for me animal cells are the better choice.
Step-by-step explanation:
Definition. Animal cells are the basic unit of life in organisms of the kingdom Animalia. They are eukaryotic cells, meaning that they have a true nucleus and specialized structures called organelles that carry out different functions.
Plant cells are the basic unit of life in organisms of the kingdom Plantae. They are eukaryotic cells, which have a true nucleus along with specialized structures called organelles that carry out different functions. Plant cells have special organelles called chloroplasts, which create sugars via photosynthesis.
What is the ordered pair of X' after point X (3, 4) is rotated 180°?
X (3,-4)
X(-3,-4)
X (-4,3)
X(-4,-3)
Answer:
X′ (−3, −4)
Step-by-step explanation:
Just took the test :)
7. Are the two triangles similar? How do you know? I need this answered quick plz
Answer:
Yes, by the angle angle rule.
Step-by-step explanation:
In the first triangle,
m<C=60 degrees, and m< D=53 degrees. You know that the sum of angles in a triangle add up to 180 degrees, so solve for E. m<E= 67 degrees.
In the second triangle,
m<F=60 degrees and m<H=67 degrees.
Since both triangle have two congruent angles, you can say that the two triangles are similiar by the AA rule.
Both triangle CDE and triangle FGH are similar to each other.
Similar figures
Two figures are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. All the corresponding angles of similar figures are congruent.
∠C + ∠D + ∠E = 180° (angles in a triangle)
60 + 53 + ∠E = 180
∠E = 67°
∠C = ∠F, ∠D = ∠G, ∠E = ∠H, hence both triangles are similar.
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a = 9 and b = 2
Work out the value of
Step-by-step explanation:
I am not sure. sorry if it is wrong
Question 8
An even function g has the point (-9,-2) on its graph.
What are the coordinates of another point on the graph of g?
Answer: (9, -2)
Step-by-step explanation:
Let's start with what makes a function even. A function is even if the graph of it is symmetric about the y-axis. What is really means is that if you were to fold your graph paper where the crease is on the y-axis, the graph should be the same on each side.
Now since g is an even function, it's correct for us to assume that it is symmetric about the y-axis. What this means is that we expect to find a value at the same point, except on the right side (because our coordinate is negative).
Our coordinate is (-9, -2). If we were to plot it, we'd see it would be in the 3rd quadrant, or the bottom left one. To be symmetrical on the right side, we know there is a point with the same coords in the 4th quadrant. To be on the right, our x coordinate would be positive, and our y coordinate will stay the same.
Hi! 8th grade math problem for you. Please see the screenshot
Answer:
r=4/2=2cm
total volume=volume of cylinder + cone=πr²h+1/3πr²h'=πr²(h+1/3 h')=2²π((10-3)+1/3× 3)=4π(7+1)=8×4π=32πcm³
Solve the equation.
-6p=48
Answer:
p=-8
Step-by-step explanation:
A negative multiplied by a negative is a positive.
Whats the answer? Please help
Answer:
Answer: y=3/2x+1
To find a line that is perpendicular, invert the slope and multiply by -1
so the original slope is -2/3,
invert it to get -3/2 then multiply by -1 to get 3/2
Put the given point (-2,-2) and the new slope into point intercept form: y+2=3/2(x+2)
Rewrite in standard form to get y=3/2x+1
Write an
equivalent expression using the distributive property.
1/4(4x - 6)
Answer:
Step-by-step explanation:
Distributive property: a*(b + c)= (a*b) + (a*c)
[tex]\frac{1}{4}(4x - 6) = 4x*\frac{1}{4} - 6*\frac{1}{4}\\\\[/tex]
[tex]= x -3*\frac{1}{2}\\\\=x - \frac{3}{2}[/tex]
How to work with this? If multiple it 12*4=48 which is not correctly.
Answer:
Step-by-step explanation:
You must have not input your units of cm^2
Answer from text book is given but I cant understand how they get this answer using these numbers?
This was the question:
Analia wants to know which school has higher academic achievements relative to the number of teachers per student.
a) What is the Graduation rate divided by teachers per student?
b) SAT average divided by teachers per student?
So I looked up the answer after getting it wrong and this is the calculations used to come to the answer. I cant figure out how they put these 3 numbers together to get 18,947 and 11,053
Answer:
The equation is
(students x points) / teachers