Answer:
4 students
Step-by-step explanation:
Let's call the total number of students in the school "x". We know that a certain percentage of them had over 80% in math, and the rest (100% - that percentage) had 80% or less.
Let's call the percentage of students who had over 80% "p". Then, we can set up the following equation:
p% of x + (100% - p%) of x = x
We can simplify this to:
p/100 * x + (100 - p)/100 * x = x
Multiplying both sides by 100 to get rid of the denominators, we get:
px + (100 - p)x = 100x
Simplifying further:
px + 100x - px = 100x
100x = 465
x = 465/100 = 4.65 (rounded to two decimal places)
So the total number of students in the school is approximately 4.65. However, we can't have a fraction of a student, so let's round up to the nearest whole number and assume there are 5 students in the school.
Now we can use the information given to find the number of students who had over 80%:
"of the students had over 80% in math"
implies that
p% of x = number of students who had over 80%
So if we plug in the values we have:
p% of 5 = number of students who had over 80%
Simplifying:
0.01p * 5 = number of students who had over 80%
0.05p = number of students who had over 80%
We don't know the value of p, but we can solve for the number of students who had over 80% for different values of p. For example:
If p = 90, then:
0.05(90) = 4.5
So 4.5 students had over 80%. Since we can't have half a student, we can assume that 4 students had over 80%.
Alternatively, we can solve for p using the information given:
"of the students had over 80% in math"
implies that
p% of x = number of students who had over 80%
So:
p% of x = number of students who had over 80%
p% of 5 = number of students who had over 80%
0.01p * 5 = number of students who had over 80%
0.05p = number of students who had over 80%
We know that the number of students who had over 80% is some integer value between 0 and 5, inclusive. We can test different values of p within this range to see if they give us an integer solution:
If p = 90, then:
0.05(90) = 4.5
This is not an integer solution, so p = 90 is not the correct answer.
If p = 80, then:
0.05(80) = 4
This is an integer solution, so p = 80 is the correct answer. Therefore, 4 students had over 80%.
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one
baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has
no effect, so the probability of a girl is 0.5. Assume that the groups consist of 45 couples. Complete parts (a) through (c)
below.
a) The value of the mean is μ = 22.5
The value of the standard deviation is σ = 3.5
b) The Value of 15 girls or fewer is significantly low.
The value of 30 girls or more is significantly high.
c) The result 36 is significantly high because 36 is greater than 30 girls. A result of 36 girls is not necessarily definitive proof of the method's effectiveness.
What is the standard deviation?The standard deviation is a measure of the amount of variability or dispersion in a set of data values. It is a statistical measure that tells you how much, on average, the values in a dataset deviate from the mean or average value.
According to the given informationa) Since the probability of having a girl for each couple is 0.5, the number of girls each couple will have can be modeled as a binomial distribution with parameters n=1 and p=0.5.
Let X be the random variable denoting the number of girls in 45 couples. Then, X follows a binomial distribution with parameters n=45 and p=0.5.
The mean of a binomial distribution is given by μ = np, so in this case, the mean number of girls in a group of 45 couples is:
μ = np = 45 x 0.5 = 22.5
Therefore, we expect to see around 22-23 girls in a group of 45 couples.
The standard deviation of a binomial distribution is given by σ = √(np(1-p)), so in this case, the standard deviation of the number of girls in a group of 45 couples is:
σ = √(np(1-p)) = √(45 x 0.5 x 0.5) = 3.535
Therefore, we can expect the number of girls in a group of 45 couples to have a standard deviation of around 3.5.
b) In this case, we can assume that the number of girls in a group of 45 couples follows a normal distribution due to the Central Limit Theorem.
Using the standard deviation we found in the previous answer (σ = 3.535), we can calculate the values that separate the results that are significantly high and significantly low.
Significantly high:
Mean + 2σ = 22.5 + 2(3.535) = 29.57
Significantly low:
Mean - 2σ = 22.5 - 2(3.535) = 15.43
c) To determine if the result of 36 girls is significantly high, we need to compare it to the values we calculated in the previous answer.
Mean + 2σ = 22.5 + 2(3.535) = 29.57
Since 36 is greater than 29.57, we can conclude that the result of 36 girls is significantly high.
This suggests that the method of gender selection may be having an effect on the probability of having a girl. However, we cannot conclusively say this without conducting further analysis or testing.
It is also important to note that the result of 36 girls is not necessarily definitive proof of the method's effectiveness.
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Write the coordinates for
each given point on the
coordinate plane below.
1. Point A
2. Point B
3. Point C
4. Point D
Answer:
Point A (-3,3)
Point B about (3,-2.75)
Point C (-4,-4)
Point D (1,0)
Step-by-step explanation:
I need this quickly please
(a)The arrow will reach a maximum height of 130 feet.
(b) After around 5 seconds, the arrow will strike the ground.
(c) At 1 second and 4 seconds after launch, the arrow will be 114 feet high.
How to determine maximum height and time?a) The maximum height of the arrow occurs at the vertex of the parabolic pathway. The x-coordinate of the vertex is given by -b/2a, where a=-16 and b=80. So, t= -b/2a = -80/(2x(-16)) = 2.5 seconds. To find the maximum height, plug in t=2.5 into the equation: h(2.5) = -16(2.5)² + 80(2.5) + 50 = 130 feet.
Therefore, the maximum height of the arrow is 130 feet.
b) To find the time it takes for the arrow to reach the ground, find the value of t when h(t)=0 (since the arrow hits the ground when h=0). We can use the quadratic formula to solve for t:
t = (-V₀ ± √(V₀² - 4ah₀)) / 2a
where a=-16, V₀=80, and h₀=50.
t = (-80 ± √(80² - 4x(-16)50)) / 2(-16) = 5 seconds or -1.5625 seconds
Since time can't be negative, the arrow will hit the ground after about 5 seconds.
c) To find the time it takes for the arrow to be 114 feet high, solve for t when h(t) = 114.
-16t² + 80t + 50 = 114
-16t² + 80t - 64 = 0
Dividing both sides by -16 gives:
t² - 5t + 4 = 0
Factoring gives:
(t-4)(t-1) = 0
So t=4 seconds or t=1 second.
Therefore, the arrow will be 114 feet high at 1 second and 4 seconds after launch.
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Silas took 18 bags of glass to the recycling center. He still has 6 bags of plastic to take to the recycling center. Which equation could be used to find x, the total number of bags of glass and plastic Silas will take to the recycling center? A. 18 - x = 6 B. x - 6 = -18 C. x - 18 = 6 D. x + 18 = 6
PLEASE HELP ME
Answer:
The correct equation to find the total number of bags of glass and plastic Silas will take to the recycling center is C. x - 18 = 6.
In this equation, x represents the total number of bags of glass and plastic Silas will take to the recycling center. The left side of the equation represents the number of bags of glass Silas will take to the recycling center (x - 18), and the right side represents the number of bags of plastic he still needs to take to the recycling center (6).
By setting the two expressions equal to each other (x - 18 = 6), we can solve for x and determine the total number of bags Silas will take to the recycling center. Adding 18 to both sides of the equation gives us x = 24, which means Silas will take a total of 24 bags (18 bags of glass and 6 bags of plastic) to the recycling center.
Which of the following can you determine, when you use deduction and start
from a given set of rules and conditions?
OA. None of these
B. What may be false
C. What may be true
D. What must be true
R
SUBMIT
Answer: D
Step-by-step explanation:
When using deduction and starting from a given set of rules and conditions, you can determine what must be true. Therefore, the correct answer is:
D. What must be true
help! I’m getting frustrated
Answer:
The domain in interval notation is (-infinity, infinity), or all real numbers.
brainliest and 20 point goes to whoever shows work that i can understand
Answer:
9. 40 = 2πr
r = 20/π inches = 6.4 inches
d = 40/π inches = 12.7 inches
10. 256 = 2πr
r = 128/π feet = 40.7 feet
d = 256/π feet = 81.5 feet
At the beach, Trevor and his sister both built sandcastles and then measured their heights. Trevor's sandcastle was 1/2 of a foot tall and his sister's was 1/5 of a foot tall. How much taller was Trevor's sandcastle than his sister's?
The height of Trevor's sandcastle is 3/10 foot taller than his sister's.
Given that, Trevor's sandcastle was 1/2 of a foot tall and his sister's was 1/5 of a foot tall.
Difference in the height of sandcastles = 1/2 - 1/5
= 5/10 - 2/10
= (5-2)/10
= 3/10
So, the difference in heights = 3/10 foot
Therefore, the height of Trevor's sandcastle is 3/10 foot taller than his sister's.
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Please help me with this math question
The first three terms of the expression (2 · x + 1 / x)¹² are 4096 · x¹², 24576 · x¹⁰ and 67584 · x⁸, respectively.
How to determine the first three terms of the power of a binomial
In this problem we find the case of a expression of the form (a + b)ⁿ, where any term of the expression can be found by binomial theorem:
[tex](a + b)^{n} = \sum\limits_{k = 0}^{n} \frac {n!}{k! \cdot (n - k)!}\cdot a^{n - k}\cdot b^{k}[/tex]
Where:
a, b - Coefficients of the binomial.n - Power of the binomial. k - Index of the term of the expanded form of the binomial.If we know that a = 2 · x, b = 1 / x and 12, then the first three terms of the power of the binomial are, respectively:
n = 0
[tex]C_{0} = \frac{12!}{0! \cdot (12 - 0)!}\cdot (2\cdot x)^{12 - 0} \cdot (\frac {1}{x})^{0}[/tex]
C₀ = 4096 · x¹²
n = 1
[tex]C_{1} = \frac{12!}{1! \cdot (12 - 1)!}\cdot (2\cdot x)^{12 - 1} \cdot (\frac {1}{x})^{1}[/tex]
C₁ = 12 · (2048 · x¹¹) · (1 / x)
C₁ = 24576 · x¹⁰
n = 2
[tex]C_{2} = \frac{12!}{2! \cdot (12 - 2)!}\cdot (2\cdot x)^{12 - 2} \cdot (\frac {1}{x})^{2}[/tex]
C₂ = 66 · (1024 · x¹⁰) · ( 1 / x²)
C₂ = 67584 · x⁸
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At the beginning of a population study, a city had 300,000 people. Each year since, the population has grown by 2.5%.
Let t be the number of years since start of the study. Let y be the city's population.
Write an exponential function showing the relationship between y and t.
All eleven letters from the word MATHEMATICS are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having the letter C written on it?
The odds against the paper having the letter C written on it is 10 : 11
What are the odds against the paper having the letter C written on it?From the question, we have the following parameters that can be used in our computation:
MATHEMATICS
In the above word, we have
Letter C = 1
letters = 11
So, the probability of C is
Probability = 1/11
When converted to odds we have
Odds = Letter - Letter C : Letters
Substitute the known values in the above equation, so, we have the following representation
Odds = 11 - 1 : 11
Evaluate
Odds = 10 : 11
Hence, the odds is 10 : 11
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The net income of the Apex Company was $110 million in 1995 and has been increasing by $30 million per year since. Over the same period, the net income of its
chief competitor, the Best Corporation, has been growing by $20 million per year, starting with $170 million in 1995. Which company earned more in 2004?
Apex Company
Best Corporation
In what year did/will Apex surpass Best?
Answer:
Step-by-step explanation:
In 2004, the net income of the Apex Company would be $110 million + ($30 million x 9 years) = $380 million.
The net income of the Best Corporation in 2004 would be $170 million + ($20 million x 9 years) = $350 million.
Therefore, Apex Company earned more in 2004.
To find the year when Apex surpassed Best, we need to set their net incomes equal and solve for time:
110 + 30t = 170 + 20t
10t = 60
t = 6
Therefore, Apex surpassed Best in the year 1995 + 6 = 2001.
Identify the domain and range of the function.
Answer:
D
Step-by-step explanation:
All the numbers that have fraction are irrational therefore the numbers are real
On a planet far far away from Earth, IQ of the ruling species is normally distributed with a mean of 110 and a standard deviation of 16. Suppose one individual is randomly chosen. Let X = IQ of an individual. find the q1 and q3
Answer:
Step-by-step explanation:
First, we need to find the z-scores for q1 and q3.
Q1:
Using the formula for z-score, we get:
z = (x - μ) / σ
where x is the IQ score we want to find the z-score for, μ is the mean IQ of the population, and σ is the standard deviation of the population.
For the first quartile (q1), we want to find the z-score such that 25% of the population has an IQ score below that value. From the standard normal distribution table, we find that the z-score corresponding to a cumulative area of 0.25 is -0.674.
So we have:
-0.674 = (x - 110) / 16
Solving for x, we get:
x = 99.8
Therefore, q1 is approximately 99.8.
Q3:
Similarly, for the third quartile (q3), we want to find the z-score such that 75% of the population has an IQ score below that value. From the standard normal distribution table, we find that the z-score corresponding to a cumulative area of 0.75 is 0.674.
So we have:
0.674 = (x - 110) / 16
Solving for x, we get:
x = 120.8
Therefore, q3 is approximately 120.8.
Find the solution to the systems \frac{m}{5}+\frac{n}{3}=0,\frac{m}{10}-\frac{7n}{6}=4
The two points on the line are (5, -9/5) and (-5/3, 3).
The other point on the line is (0, -12/7).
What is system of equations?The equation [tex]\frac{m}{5} +\frac{n}{3} =0[/tex] can be rewritten as:
3m + 5n = 0
When m=5:
3m + 5n = 0
3(5) + 5n = 0
n = -9/5
Simplify the above equation,
When n=3:
3m + 5n = 0
3m + 5(3) = 0
m = -5/3
the two points on the line are (5, -9/5) and (-5/3, 3)
The equation [tex]\frac{m}{10} -\frac{7n}{6} =4[/tex] can be simplified as follows:
m/10 - 7n/6 = 4
m/10 = 7n/6 + 4
m = 70n/6 + 40
m = 35n/3 + 20
When n=0:
m = 35n/3 + 20
m = 20
So, the point on the line is (20, 0).
When m=0:
35n/3 + 20 = 0
35n/3 = -20
n = -12/7
So, the other point on the line is (0, -12/7).
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The fox population in a certain region has an annual growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 14400.
The function that models the population t years after 2000 is P(t) = 14400 * (1.04)^t
How find a function that models the population t years after 2000?The population growth function is of the form:
P(t) = P₀ * (1 + r)^t
Where:
P(t) is the current population after t years
P₀ is the starting population
r is the annual growth rate in percent
Thus, P₀ = 14400 and 4% = 0.04
P(t) = P₀ * (1 + r)^t
P(t) = 14400 * (1 + 0.04)^t
P(t) = 14400 * (1.04)^t
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Complete Question
The fox population in a certain region has an annual growth rate of 4 percent per year. It is estimated that the population in the year 2000 was 14400.
a) Find a function that models the population t years after 2000 (t=0 for 2000).
Your answer is P(t) =
- Higher Order Thinking A sporting goods store manager was selling
a kayak set for a certain price. The manager offered the markdowns
shown on the right, making the one-day sale price of the kayak set $328.
Find the original selling price of the kayak set.
KANN &
SET
10%
OFF
TRRAY
EXTRA
30%
OFF
The original selling price of the kayak set, given the discounts, would be $ 520. 63
How to find the original selling price ?The kayak is being sold such that a discount was offered of 10 % and then an additional discount was offered for 30 %.
The first step to the original price is:
= 328 / ( 1 - 30 %)
= 328 / 0. 70
= $ 468. 57
Then, the original price, would then account for the original discount of 10 % to become:
= 468. 57 / ( 1 - 10 %)
= 468. 57 / 0. 90
= $ 520. 63
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In 2022, a random sample of UGA students found that they slept an average of 7.43 hours per night. The margin of error for a 90% confidence interval was reported as 1.32 hours.
(a) What is the lower limit of this 90% confidence interval?
lower limit = (2 decimal places)
(b) If 500 random samples like this were selected, and a 90% confidence interval was constructed using each sample, approximately how many of these confidence intervals would contain the population mean?
(whole number)
Step-by-step explanation:
(a) The lower limit of the 90% confidence interval can be calculated using the formula:
lower limit = sample mean - margin of error
Plugging in the given values, we have:
lower limit = 7.43 - 1.32
lower limit = 6.11 (rounded to 2 decimal places)
Therefore, the lower limit of the 90% confidence interval is approximately 6.11 hours per night.
(b) If 500 random samples like this were selected, and a 90% confidence interval was constructed using each sample, the expected number of intervals that would contain the population mean can be approximated using the margin of error as a guide.
Since the margin of error is 1.32 hours, we can expect roughly 90% of the confidence intervals to contain the true population mean. Therefore, out of 500 samples, we would expect approximately:
500 * 0.9 = 450
So, approximately 450 of these confidence intervals would contain the population mean.
If the length of BE is 3x-11 and the length of CD is 9x - 43, what is the length of CD?
The value of line CD is 20
How to determine the valueFrom the diagram shown, we have that;
Line BE = 3x - 11
Line CD = 9x - 43
Note that the length of line BE is half the length of line CD
this is represented as;
2BE = CD
Now, substitute the values
2(3x - 11) = 9x - 43
expand the bracket
6x - 22 = 9x - 43
collect the lie terms
6x - 9x = -43 + 22
-3x = -21
Make 'x' the subject
x = 7
Then, CD = 9(7) - 43 = 20
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Find x,y if (x-1) 8i = 5 + (y² - 1) i
A stack of two hundred eighty cards is placed next to a ruler, and the height of stack is measured to be 7/ 8 inches. How thick is one card?
In a case whereby stack of two hundred eighty cards is placed next to a ruler, and the height of stack is measured to be 7/ 8 inches the thickness of one card is 1/320 inches
How can the thickness be known?Based on the provided information, two hundred eighty cards is placed next to a ruler ten we can set up the expression as
( 7/ 8) / 280
7/ 8 * 1/280
1/320
Therefore, based on the given information, this implies that Each card is 1/320 inches
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Can I get some help with these problems??
A) (2x+1)⁰ = 96⁰
=> 2x = 96⁰ - 1⁰ = 95⁰
=> x = 95⁰/2 = 47⁰30' (= 47.5⁰)
B) x⁰ = (2x-7)⁰
=> x - 2x = -7
=> -x = -7
=> x = 7⁰
C) mIJ = 45⁰ ; mJK = 57⁰
m✓ IJK = 180⁰- 45⁰ - 57⁰ = 78⁰
=> mIK = 78⁰
Ans: a) 47.5⁰ b) 7⁰ c) mIJ = 45⁰ ; mJK = 57⁰ ; mIK = 78⁰
Ok done. Thank to me >:333
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d = 163t
D. d = 81.50t
Answer:
B
Step-by-step explanation:
163 money t for time 2 for 2hours
What is the length of side c? (Hint: There are 2 angles and 2 sides)
The length of side c is approximately 4.62 units.
How to solveCalculating the value of side c can be done by applying the Law of Sines on two angles and two sides.
Initially, determining angle C is necessary:
The corresponding formula for Angle C: 180° - (Angle A + Angle B) evaluates to 90° after substituting in reference values; 60°, and 30° respectively.
Implementing the Law of Sines culminates in this expression:
a/sin(A) = b/sin(B) = c/sin(C)
Replace with known angles and evaluate as follows:
Since the measures are known;
c/sin(C) = a/sin(A).
Subsequently,
by simple algebra c= a * sin(C) / sin(A) leads to desired outcome.
Putting relevant points into the equation above gives:
c = 4 * sin(90°) / sin(60°)
By using sine values from a calculator:
the preceding expression becomes,
c = 4 * 1 / (sqrt(3)/2)
After solving for c:
c = 8 / sqrt(3)
Using square root's rationalization: multiply numerator, and denominator by √3 resulting in
c = (8 * sqrt(3)) / 3
The length of side c is approximately 4.62 units.
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Let's assume we have a triangle with angles A and B and sides a and b, where angle A is opposite to side a, and angle B is opposite to side b. Given angle A = 60°, angle B = 30°, side a = 4 units, and side b = 2 units, find the length of side c.
If you multiply or divide both sides of an inequality by a negative number you must_______ the inequality sign
Answer:
reverse or flip
Find the perimeter and area of a square if the length of its diagonal is 16 mm. Round your answers to the nearest tenth. (Hint: Draw and label the square)
The solution is : the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².
Here, we have,
Use the basic 45-45-90 triangle with side length 1 as the building block here. If the length of one side is 1, then the perimeter is 1 + 1 + 1 + 1, or 4, and the length of the diagonal is √2.
We are told that the length of the diagonal of the given square is 16 m.
Determine the length of one side of this square, using an equation of proportions:
16 x
------ = -------
√2 1
16
Then (√2)x = 16, and x = -----------
√2
The perimeter of the given square (with diagonal 16 mm) is 4 times the side length found above, or:
16 16
4 ---------- = (2)(2) ----------- = (2)(√2)(16) = 32√2 (all measurements in mm)
√2 √2
This perimeter, rounded to the nearest tenth, is 45.3 mm.
so, area of the square is:
(16/√2)² = 512mm².
Hence, The solution is : the perimeter and area of a square if the length of its diagonal is 16 mm is, 45.3 mm and 512mm².
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What is the sum of the polynomials?
17m-12n-1
+ 4-13m-12n
Answer: 4m-24n+3
Step-by-step explanation:
Expand and collect like terms!
[tex](17m-12n-1) + (4-13m-12n)\\= 17m - 12n - 1 + 4 - 13m - 12n\\=4m-24n+3[/tex]
Hope this helps <3
Numbers in the octal number system are numbered from 0 to 7. Based on the numbering pattern in the decimal number system, list the next 20 octal numbers
The next 20 octal numbers after 7 are: 10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33
How to determine the next 20 octal numbersIn the decimal system, we count from 0 to 9 before moving to the next place value. In the octal system, we count from 0 to 7 before moving to the next place value. Therefore, the next 20 octal numbers after 7 are:
10, 11, 12, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 32, 33
To understand how this pattern works, consider the decimal number 32. To convert it to octal, we can repeatedly divide it by 8 and record the remainders:
32 ÷ 8 = 4 with remainder 0
4 ÷ 8 = 0 with remainder 4
So the octal representation of 32 is 40. Similarly, we can convert any decimal number to octal by repeatedly dividing by 8 and recording the remainders.
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Shen bought a desk on sale for $218.40. This price was 72% less than the original price. What was the original price?
Answer:
780
Step-by-step explanation:
In this example we will call Original Price = y
72%=0.72
218.40=0.72*y
1-0.72=0.28
218.4÷0.28=780
1. Each person in a random sample of 1.026 adults in the United States was asked the following question "Based on what you know about the Social Security System today, what would you like Congress and the President to do during this next year? The response choice and the percentages selecting them are shown below
Completely overhaul the system 19%
Make some major changes 39%
Make some minor adjustments 30%
Leave the system the way it is now
No opinion 1%
Find a 95% confidence interval for the proportion of all United States adults who would respond "Make some major changes to the question
a. Identify the variables needed to solve the problem.
b. Can a normal distribution be used to approximate this data Justify your evidence. c. Find the standard deviation
d. Calculate the point estimate and margin of error
e. calculate the confidence interval
Answer:
Step-by-step explanation:
a. Variables needed to solve the problem:
Sample size: n = 1,026
Proportion of the sample that responded "Make some major changes": p = 0.39
Confidence level: 95%
b. To determine if a normal distribution can be used to approximate the data, we need to check if the sample size is large enough to meet the requirements for a normal approximation. The sample size should be at least 10 times larger than the number of successes (np) and 10 times larger than the number of failures (n(1-p)). In this case, we have:
np = 1026 x 0.39 = 399.14
n(1-p) = 1026 x 0.61 = 626.86
Both np and n(1-p) are greater than 10, so we can assume that a normal distribution can be used to approximate the data.
c. The standard deviation of the proportion can be calculated using the following formula:
standard deviation = sqrt(p(1-p) / n)
standard deviation = sqrt(0.39 x 0.61 / 1026) = 0.024
d. The point estimate of the proportion of all United States adults who would respond "Make some major changes" is simply the sample proportion, which is p = 0.39. The margin of error can be calculated using the following formula:
margin of error = z* * standard deviation
where z* is the z-score associated with the 95% confidence level. Using a standard normal distribution table or a calculator, we find that the z-score for a 95% confidence level is approximately 1.96. Therefore:
margin of error = 1.96 * 0.024 = 0.047
e. The confidence interval can be calculated using the following formula:
confidence interval = point estimate ± margin of error
confidence interval = 0.39 ± 0.047
confidence interval = (0.343, 0.437)
Therefore, we are 95% confident that the proportion of all United States adults who would respond "Make some major changes" is between 0.343 and 0.437.