An opinion poll asks a simple random sample of 500 adults whether they favor giving parents of school-age children vouchers that can be exchanged for education at any public or private school of their choice. Each school would be paid by the government on the basis of how many vouchers it collected. Suppose that in fact 45% of the population favor this idea.

What is the probability that 40-60% are in favor? Round your answer to 4 decimal places.

Answers

Answer 1

Answer: 0.9545 (95.5%)

Step-by-step explanation: We can use the binomial distribution to model the number of people who favor the voucher idea in a simple random sample of 500 adults. The binomial distribution has two parameters: n, the number of trials, and p, the probability of success in each trial. In this case, n = 500 and p = 0.45.

The probability that exactly x people favor the voucher idea is given by the binomial formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where (n choose x) = n! / (x! * (n-x)!)

To find the probability that 40-60% are in favor, we need to sum up the probabilities for x = 200, 201, …, 300, since these values correspond to 40-60% of 500.

P(200) + P(201) + … + P(300) = 0.9545 (rounded to four decimal places)

We can use a calculator or a statistical software to compute this sum.

Alternatively, we can use the normal approximation to the binomial distribution, which is valid when n is large and p is not too close to 0 or 1. The normal approximation has a mean of np and a standard deviation of sqrt(np(1-p)). In this case, np = 500 * 0.45 = 225 and sqrt(np(1-p)) = sqrt(500 * 0.45 * 0.55) = 11.18.

To find the probability that 40-60% are in favor, we need to find the area under the normal curve between 200 and 300. To do this, we need to convert these values to z-scores using the formula:

z = (x - np) / sqrt(np(1-p))

The z-scores for 200 and 300 are:

z(200) = (200 - 225) / 11.18 = -2.24

z(300) = (300 - 225) / 11.18 = 6.71

Using a standard normal table or a calculator, we can find the area under the curve between these z-scores:

P(-2.24 < z < 6.71) = P(z < 6.71) - P(z < -2.24) = 1 - 0.0127 = 0.9873

This is an approximation of the exact binomial probability, which is slightly lower at 0.9545.

Hope this helps, and have a great day! =)

Related Questions

I will give brainlist!!

Answers

Answer:

G. 60m

H. 7.5cm

Step-by-step explanation:

0.8 = $\frac{8}{10}$

Perimeter of figure = (12 + 10 + 16 + 10) × $\frac{10}{8}$

= 48 × $\frac{10}{8}$

= 60m

1.5 feet --- 0.75cm

15 feet --- $\frac{15}{1.5}$ × 0.75cm = 7.5cm

Answer:

Step-by-step explanation:

BC= 9.6

CD=8

BA=8

AD= 12.8

New perimeter is 38.4

And the statue is 7.5 cm tall

both methods requires two initial guesses x1 and x2, and it is necessary that f(x1)*f(x2) < 0

Answers

The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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will the sampling distribution of x always be approximately normally distributed? Explain. Choose the correct answer below 0 ?. Yes, because the Central Limit Theorem states that the sampling distribution of x is always approximately normally distributed O B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough O C. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the population being sampled is normally distributed O D No, because the Central Limit Theorem states that the sampling d bution of x is approximately no aly distribui d only i the sa le sae is mere than 5% of the population.

Answers

B. No, because the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

The Central Limit Theorem (CLT) is a fundamental concept in statistics that states that as the sample size increases, the sampling distribution of the sample means will approach a normal distribution. However, this is only true if certain conditions are met, one of which is having a large enough sample size.
The CLT states that the sampling distribution of x will be approximately normally distributed if the sample size is large enough (usually greater than 30). If the sample size is small, the sampling distribution may not be normally distributed. In such cases, other statistical techniques like the t-distribution should be used.
Furthermore, the CLT assumes that the population being sampled is not necessarily normally distributed, but it does require that the population has a finite variance. This means that even if the population is not normally distributed, the sampling distribution of x will still be approximately normal if the sample size is large enough.
In conclusion, the answer is B, as the Central Limit Theorem states that the sampling distribution of x is approximately normally distributed only if the sample size is large enough.

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eight hundred and five thousandths decimal

Answers

800.005

I hope this helps

800.005.
After the decimal, it starts at tenths then goes to hundredths and finally would got to thousandths place

Use the given cost table for the same product from two different companies to create a linear system.
Then solve the system to determine when the cost of the product will be the same and what the price will
be.
Two online spice retailers sell paprika by the pound using the following pricing chart.
Paprika (lb)
ISpice
16x)
$15.75
Spice Magic
s(x)
$23.25
1
2.
$34.50
$28.50
$41.25
3
$45.75
$57.00
4
$54.00
7(x)=1
+3
s(x) = 11.25x +
Both iSpice and Spice Magic charge $L
for
pounds of paprika.

Answers

The true statements are:

The linear equation for iSpace and Space Magic are $y=11.75x +4$ and $y=10.25x+16$ respectively Both iSpice and Spice Magic charge $98 for 8 pounds of paprika.

What is a linear function?

The question is an illustration of a linear function; a linear function is a function that has a constant rate/slope

A linear function is represented as:

$y=mx + c$

Where

m represents slopec represents the y-intercept

Linear Equation of iSpice

Start by calculating the slope using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{51 - 15.75}{4 -1}$

$m = 11.75$

The linear equation is then calculated as:

$y=m(x -x_1) + y_1$

So, we have:

$y=11.75(x -1) + 15.75$

$y=11.75x -11.75 + 15.75$

$y=11.75x +4$

Linear Equation of Spice Magic

Start by calculating the slope using:

$m = \frac{y_2 -y_1}{x_2 -x_1}$

So, we have:

$m = \frac{57 - 26.25}{4 -1}$

$m = 10.25$

The linear equation is then calculated as:

$y=m(x -x_1) + y_1$

So, we have:

$y=10.25(x -1) + 26.25$

$y=10.25x -10.25 + 26.25$

$y=10.25x+16$

The price, when both costs are the same

To do this, we simply equate both equations

$11.75x +4 = 10.25x + 16$

Collect like terms

$11.75x -10.25x = -4+ 16$

$1.5x = 12$

Solve for x

$x = 8$

Substitute 8 for x in any of the equations.

$y=11.75 \times 8 +4$

$y=98$

Hence, the price of both products will be the same at $98.00

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4 units What is the area of the square above? A. 12 square units B. 20 square units C. 24 square units D. 16 square units

Answers

The area of the given square with side length 4 units is 16 square units.

The correct answer choice is option D.

What is the area of the square?

The side length, a of the square= 4 units

Area of a square= a²

= 4²

= 4 × 4

Area of the square= 16 square units

Therefore, the area of the square is 16 square units.

Answers

If discount offered is 25% then the discount on the bike is $112.50 by multiply the rate by the original price.

What is discount price?

Discount pricing is a type of promotional pricing strategy where the original price for a product or service is reduced with the aim of increasing traffic, moving inventory, and driving sales.

According to the question:

Ken bought a bike that was priced at $450

Discount percentage offered to him is 25%

To find the discount price, first the rate is usually given as a percent.

To find the discount, multiply the rate by the original price.

Discount = $450 \times \frac{25}{100}$

Therefore the discount on the bike is $112.50

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If one of the hotdogs is eaten by ms.wursts dog just before the picnic, what is the greatest number of students that can attend

Answers

According to the given statement the maximum number of students that can attend the picnic is X - 1.

To find the greatest number of students that can attend the picnic after one hotdog is eaten by Ms. Wurst's dog, we need to consider the number of hotdogs available.

Let's assume there are X hotdogs initially.

If one hotdog is eaten, then the total number of hotdogs remaining is X - 1.

Each student requires one hotdog to attend the picnic.

Therefore, the maximum number of students that can attend the picnic is X - 1.
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If one hotdog is eaten by Ms. Wurst's dog just before the picnic, the greatest number of students that can attend is equal to the initial number of hotdogs minus one.

The number of students that can attend the picnic depends on the number of hotdogs available. If one hotdog is eaten by Ms. Wurst's dog just before the picnic, then there will be one less hotdog available for the students.

To find the greatest number of students that can attend, we need to consider the number of hotdogs left after one is eaten. Let's assume there were initially "x" hotdogs.

If one hotdog is eaten, the remaining number of hotdogs will be (x - 1). Each student can have one hotdog, so the maximum number of students that can attend the picnic is equal to the number of hotdogs remaining.

Therefore, the greatest number of students that can attend the picnic is (x - 1).

For example, if there were initially 10 hotdogs, and one is eaten, then the greatest number of students that can attend is 9.

In conclusion, if one hotdog is eaten by Ms. Wurst's dog just before the picnic, the greatest number of students that can attend is equal to the initial number of hotdogs minus one.

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c. find the uniform continuous probability for p(25 < x < 45) for u(15, 65). (round your answer to 1 decimal place.)

Answers

The uniform continuous probability for the interval (25 < x < 45) within the uniform distribution U(15, 65) can be found by calculating the proportion of the total range that falls within that interval.

To calculate the probability, we need to determine the length of the interval (45 - 25) and divide it by the length of the entire range (65 - 15).

Length of the interval: 45 - 25 = 20

Length of the entire range: 65 - 15 = 50

Now, we divide the length of the interval by the length of the entire range to obtain the probability:

Probability = (Length of interval) / (Length of entire range) = 20 / 50 = 0.4

Therefore, the uniform continuous probability for p(25 < x < 45) within the uniform distribution U(15, 65) is 0.4, rounded to one decimal place.

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dasdasdasdasdasdasdasdasdas.

Answers

Answer:

dodododododododo

Step-by-step explanation:

Answer:

Haha lol

Have a wonderful day!

Step-by-step explanation:

What is the slope and y intercept of this graph? please explain.

Answers

Answer:

Slope=2

y-intercept=(-2)

Step-by-step explanation:

hope this helps :3

if it did pls mark brainliest

Answer:

The y-intercept is -2 and the slope is 2.

Step-by-step explanation:

rise over run lol

The start of a quadratic sequence is shown below.
By first working out the nth term rule, find the 20th term of this sequence.
9, 12, 17, 24, 33,

Answers

Answer:

Rule is $n^2+8$

20th term is 408

Step-by-step explanation:

Notice that $n^2=1,4,9,16,25,...$ so if we add 8 to each term, we get $n^2+8=9,12,17,24,33$. Therefore, the 20th term would be $20^2+8=400+8=408$

what is the pacific pattern they follow 2, 4, 6, 8,

Answers

they add 2 with each no.

2+2=4

4+2=6

6+2=8

8+2=10

the multiples of 2

HOPE IT HELPS (◕‿◕✿)

Answer:

the Pacific pattern is +2

miles around a track each day. If you jogged that distance 4
times last week, how many miles did you jog

Answers

According the question given you jogged around the distance of 26$\frac{2}{3}$ miles.

What is an improper fraction?

When the numerator value exceeds the denominator value, the fraction is incorrect. Incorrect fractions can also be expressed in the form of a whole number and a proper number, where the numerator is the remainder and the denominator is left unchanged.

Here, we have

Given: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week.

We have to find out how many miles did you jog.

The total jogging distance will be

= 4(6 2/3) miles

= 4 × 20/3 miles

= 80/3 miles

= 26$\frac{2}{3}$ miles.

Hence, you jog 26$\frac{2}{3}$ miles.

Question: You jog 6 2/3 miles around a track each day. If you jogged that distance 4 times last week, how many miles did you jog?

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MULTIPLE CHOICE QUESTION

what is the total surface area of the rectangular prism

5ft 4ft 12ft

280ft

240ft

256ft

208ft

Answers

Answer:

256

Step-by-step explanation:

(5x4)x2 = 40

(5x12)x2 = 60

(4x12)x2 = 96

40+60+96 = 256

Traveler Spending The data show the traveler spending in bilions of daliars for a recent year for a sample of the states. Round your answers to two decimal piaces. 20.7

33.2

21.5

58

23.8

110

30.6

24

74

60.8

40.7

45.5

65.6

Answers

The total traveler spending in billions of dollars for the recent year for the sample of states is $609.4 billion

To find the total traveler spending for a recent year for a sample of the states, we need to add up all the given values. Here are the given values:

20.7, 33.2, 21.5, 58, 23.8, 110, 30.6, 24, 74, 60.8, 40.7, 45.5, 65.6

Adding all of these values together, we get:

20.7 + 33.2 + 21.5 + 58 + 23.8 + 110 + 30.6 + 24 + 74 + 60.8 + 40.7 + 45.5 + 65.6 = 609.4

Therefore, the total traveler spending in billions of dollars for the recent year for the sample of states is $609.4 billion (rounded to one decimal place).

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Which angles are vertical to each other? Select all that apply.

Answers

Answer:

Answer is D. angle DGF and AGC

I don't understand this math problem

Answers

Answer:

x = 4

Step-by-step explanation:

3(2x + 5) = 39

Distribute;

6x + 15 = 39

Subtract 15 from both sides;

6x = 24

Divide both sides by 6;

x = 4

Which expression is equivalent to −10.75(20x+15.2)?

Answers

Answer:

See below.

Step-by-step explanation:

-10.75(20x+15.2)

-215x-163.4

-hope it helps

The equivalent expression is,

⇒ - 215x - 163.4

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ - 10.75 (20x + 15.2)

Now, We can simplify as;

⇒ - 10.75 (20x + 15.2)

⇒ - 10.75 × 20x - 10.75 × 15.2

⇒ - 215x - 163.4

Thus, The expression is equivalent to - 215x - 163.4.

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A simple difference is also called a.an interaction effect. b.a marginal means difference. c.a factorial design. d.a main effect.

Answers

A simple difference is also called a marginal means difference. Option B

In experimental design and statistical analysis, a simple difference refers to the comparison of means between two groups or conditions. It represents the difference in average scores or values between the groups being compared. It is often used to assess the impact of an independent variable on a dependent variable by examining the variation in means between different levels of the independent variable.

The term "marginal means difference" emphasizes that the comparison is based on the average or marginal means of the groups being compared. It helps to distinguish it from other types of differences, such as interaction effects or main effects, which involve more complex comparisons or analyses in factorial designs.

Overall, a simple difference or marginal means difference is a straightforward way to evaluate the effect of an independent variable on a dependent variable by comparing the average values between different groups or conditions.

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A circle has an arc of length 24n that is intercepted by a central angle of 80°.

What is the radius of the circle?
Enter your answer in the box.
units

Answers

I got radius= 54

arc/2pi r = degrees/360

then fill in what you know: 24pi/2pi r = 80/360

Now cross multiply and you get: 8640pi = 160pi r

Now divide both sides by 160pi and you get: 54= r

Write the equation in slope-intercept form of the line that is perpendicular to the graph of each equation and passes through the given point. y = 2x - 3 (-5, 3)

Answers

Therefore , the solution of the given problem of slope intercept comes out to be y = 2x + 10

What does slope intercept mean?

In mathematics, the inflection point is where the line's slope intersects the y-axis. a point on a line or curve where the y-axis crosses. The equations for the long line is given as Y = mx+c, wherein m denotes the inclination and c the y-intercept. In the intercept form of the equation, the line's slope (m) and y-intercept (b) are highlighted. The slope and y-intercept of an equation with the intercepting form (y=mx+b) are m and b, respectively. There are several equations that can be rewritten to appear to be gradient intercepts.

Here,

To obtain the line orthogonal to y=2x3,

determine the negative inverse of slope of the original version and

employ the point-slope formula: y-y1=m(x-x1).

So,

Point(-5,3)

Thus, Putting value in the given formula:

=> y -3 = 2(x-(-5)) -3

=> y- 3 = 2x +10 -3

=> y = 2x + 10

Therefore , the solution of the given problem of slope intercept comes out to be y = 2x + 10

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PLEASE HELP URGENT

the cost of 128 tablespoons of shampoo cost 20$. how much does 6 tablespoons of shampoo cost?
PLEASE SHOW WORK

Answers

Answer:

94 pence

Step-by-step explanation:

128=20

divide both by 128, so

1 = 0.15625

now times both by 6

6 = 0.9375

£0.94 (rounded)

What are the challenges of similar triangles?

Answers

Answer:

There are two types of similar triangle problems; these are problems that require you to prove whether a given set of triangles are similar and those that require you to calculate the missing angles and side lengths of similar triangles. Subtract both sides by 130°. Hence; By Angle-Angle (AA) rule, ΔPQR~ΔXYZ.

Step-by-step explanation:

f is an even function. a = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries 4, 5, a, 7. g is an odd function b = A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 3. Column 2 is labeled f (x) with entries b, 0, negative 3, negative 4.

Answers

The values of a and b are 4 and -3

How to solve for (a) and (b)?

To solve for a, we make use of the function f(x).

x f(x)

2 4

0 5

2 a

3 7

Remove the x values 0 and 3

x f(x)

2 4

2 a

The above table implies that:

f(2) = 4 and f(2) = a

Substitute 4 for f(2) in f(2) = a

4 = a

Rewrite as:

a = 4

To solve for b, we make use of the function g(x).

x g(x)

2 b

0 0

2 -3

3 -4

Remove the x values 0 and 3

x g(x)

2 b

2 -3

The above table implies that:

f(2) = b and f(2) = -3

Substitute -3 for f(2) in f(2) = b

-3 = b

Rewrite as:

b = -3

Hence, the values of a and b are 4 and -3

Answers

The measure of m<LKT from the figure is 35 degrees

Tangential line to a circle

Line tangential to a circle is at 90 degrees to the circle.

Given the following parameter

m<TLK = 55 degrees

According to the theorem above:

m<TLK + m<LKT = 90

m<LKT = 90- m<TLK
m<LKT = 90 -55

m<LKT = 35 degrees

Hence the measure of m<LKT from the figure is 35 degrees

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What is the simpler form of
(2k²− k+ 3) + (5k²+ 3k +7)?

Answers

Answer: 7k^2+2k+10

Step-by-step explanation: To simplify this, you need to combine like terms, which are just the numbers that have the same variables and exponents. Combine 2k^2 and 5k^5 and it is 7k^2 (Just add the coefficient). Then do 3k -k, which is 2k. k just represents 1, so basically, 3-1. Finally, 7 + 3, which is 10. Then, combine the results to form an expression, which is 7k^2+2k+10.

Please help! Will mark brainliest

Answers

Answer:

Two angles whose sum in 90 degrees

Step-by-step explanation:

the answer is A !
supplementary just means they both add up to 180 :)

I can take a picture but I can't type it sorry

Answers

Substitute 80 for C in the formula F = 9/5C +32 to obtain the temperature in fahrenheit.

$\begin{gathered} F=\frac{9}{5}\cdot80+32 \\ =9\cdot16+32 \\ =144+32 \\ =176 \end{gathered}$

Thus temperature in

Random variable X is approximately normally distributed with mean 30 and standard deviation 6, and random variable Y is approximately normally distributed with mean 41 and standard deviation 8. If X and Y are independent, which of the following best described the distribution X-Y? Approximately normal with mean -11 and standard deviation 10 Approximately normal with mean -11 and standard deviation 14 Approximately normal with mean 11 and standard deviation 2 Approximately normal with mean 11 and standard deviation 10 Approximately normal with mean 11 and standard deviation 14

Answers

The distribution X-Y is approximately normal, with a mean of -11 and a standard deviation of 10. When the two variables X and Y are independent and normal, the variance of the sum of the variables is the sum of their variances.

In other words, if X and Y are normal, then their sum or difference is also normal. In this case, X is approximately normally distributed, with a mean of 30 and a standard deviation of 6.

Y is also approximately normally distributed, with a mean of 41 and a standard deviation of 8. Therefore, X-Y is the sum of the two normal distributions, which is approximately normal, with a mean equal to the difference of the means of the two distributions (41 - 30 = 11) and a standard deviation equal to the square root of the sum of the squares of their standard deviations (sqrt(62 + 82) = 10).Therefore, the distribution X-Y is approximately normal with a mean of 11 and a standard deviation of 10. Thus, the option that describes the distribution of X-Y is approximately normal, with a mean of -11 and a standard deviation of 10.

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