An 80% confidence interval for a proportion is found to be (0.27, 0.33). Whatis the sample proportion?

Answers

Answer 1

Step 1

Given;

Step 2

When repeated random samples of a certain size n are taken from a population of values for a categorical variable, the mean of all sample proportions equals the population percentage (p).

[tex]\begin{gathered} Sample\text{ proportion=}\hat{p} \\ \hat{p}\pm margin\text{ error=cofidence interval} \end{gathered}[/tex]

Thus;

[tex]\begin{gathered} Let\text{ }\hat{p}=x \\ Margin\text{ of error=y} \\ x-y=0.27 \\ x+y=0.33 \end{gathered}[/tex]

checking properly, the sample proportion =0.30, because

[tex]\begin{gathered} 0.30-0.03=0.27 \\ 0.30+0.03=0.33 \end{gathered}[/tex]

Answer; Option D

[tex]0.30[/tex]

Related Questions

If f(x) = 2x+3, what is f(-2)

Answers

Answer: f(-2) = -1

Step-by-step explanation:

2x + 3

2(-2) +3

-4 + 3

-1

Answer:

Step-by-step explanation:

you plug in the -2 to the equation for x

f(-2)= 2(-2)+3

f(-2)=-1

Give the sample space describing all the outcomes. Then give all of the out comes for the event that the number 3 chosen. Use the format H1 to mean that the coin toss is heads and the number chosen is 1. If there is more than one element in the set separate them with commas

Answers

Explanation

The sample space is composed of all the possible outcomes i.e. of all the possible combinations between the result of tossing the coin and picking the card. There are two possible outcomes for the coin and four for the cards so there will be 8 different combinations in the saple space. These are:

[tex]H1,H2,H3,H4,T1,T2,T3,T4[/tex]

Then we must show all the outcomes where the card with the 3 is picked. This set is composed of all the elements with a 3 in the list above. There are two:

[tex]H3,T3[/tex]Answers

Then the answers are:

Sample space: {H1,H2,H3,H4,T1,T2,T3,T4}

Event that the number chosen is 3: {H3,T3}

the top of the hill rises 67 feet above checkpoint 4, which is -211. What is the altitude of the top of the hill?

Answers

Answer:

-144 feet

Step-by-step explanation:

-211 plus the added 67 feet it is above equals an altitude of -144ft

I need help with a math assignment. i linked it below

Answers

Since Edson take t minutes in each exercise set

Since he does 6 push-ups sets

Then he will take time = 6 x t = 6t minutes

Since he does 3 pull-ups sets

Then he will take time = 3 x t = 3t minutes

Since he does 4 sit-ups sets

Then he will take time = 4 x t = 4t minutes

To find the total time add the 3 times above

Total time = 6t + 3t + 4t

Total time = 13t minutes

The time it takes Edison to exercise is 13t minutes

please help me please

Answers

F (x) = (-1/20)x + 13.6

Then

Radmanovics car y -intercept is= 13.6 gallons

Mr Chin's car y-intercept is= 13.2

Then , in consecuence

Radmanovics car has a larger tank, than Mr Chin's car.

Answer is OPTION D)

Help me please what is the probability of all the letters?

Answers

Given:

• Number of male who survived = 338

• Number if female sho survived = 316

• Number f children who survived = 57

• Number of male who died = 1352

• Number of female who died = 109

• Number of children who died = 52

• Total number of people = 2224

Let's solve for the following:

(a). Probability of the passenger that survived:

[tex]P(\text{survived)}=\frac{nu\text{mber who survived}}{total\text{ number if people }}=\frac{711}{2224}=0.320[/tex]

(b). Probability of the female.

We have:

[tex]P(\text{female)}=\frac{\text{ number of females}}{total\text{ number }}=\frac{425}{2224}=0.191[/tex]

(c). Probability the passenger was female or a child/

[tex]P(\text{female or child)}=\frac{425}{2224}+\frac{109}{2224}=\frac{425+109}{2224}=0.240[/tex]

(d). Probability that the passenger is female and survived:

[tex]P(femaleandsurvived)=\frac{316}{2224}=0.142[/tex]

(e). Probability the passenger is female and a child:

[tex]P(\text{female and child)=}\frac{425}{2224}\times\frac{109}{2224}=0.009[/tex]

(f). Probability the passenger is male or died.

[tex]P(male\text{ or died) = P(male) + }P(died)-P(male\text{ and died)}[/tex]

Thus, we have:

[tex]P(\text{male or died)}=\frac{1690}{2224}+\frac{1513}{2224}-\frac{1352}{2224}=0.832[/tex]

(g). If a female passenger is selected, what is the probability that she survived.

[tex]P(\text{survived}|\text{female)}=\frac{316}{425}=0.744[/tex]

(h). If a child is slelected at random, what is the probability the child died.

[tex]P(died|\text{ child)=}\frac{52}{109}=0.477[/tex]

(i). What is the probability the passenger is survived given that the passenger is male.

[tex]=\frac{338}{1690}=0.2[/tex]

ANSWER:

• (a). 0.320

• (b). 0.191

• (c). 0.240

• (d). 0.142

• (e). 0.009

• (f). 0.832

• (g) 0.744

• (h). 0.477

• (i) 0.2

he multiplication table below can be used to find equivalent ratios.

A multiplication table.

Which ratio is equivalent to the ratio 18:24?
15:20
20:15
30:36
36:30

Answers

Answer:

15:20

Step-by-step explanation:

18:24 can be written [tex]\frac{18}{24}[/tex] if I simplify this by dividing the top and bottom by 6, I get [tex]\frac{3}{4}[/tex]

I am looking for what other ration will reduce to [tex]\frac{3}{4}[/tex]

[tex]\frac{15}{20}[/tex] Divide the top and bottom by 5 and you will get [tex]\frac{3}{4}[/tex]

Which inequality is represented by the graph?

Answers

Answer:

A. x > -1

Step-by-step explanation:

x > -1

-------------->

<----0------------->

-1

x < -1

<-------

<------0------------>

-1

x ≥ -1

---------->

<---------|---------->

-1

x ≤ -1

<----------

<---------|---------->

-1

< and > represent an open circle

≤ and ≥ represent a closed circle

I hope this helps!

1) find the value of AC
2) find the measure of

Answers

1) The value of AC = 116

2) The measure of ∠BEF = 53°

What is Bisector?

When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.

Given,

BD is a perpendicular bisector

A is an angle bisector

BD is a perpendicular bisector then AD = DC

2n + 18 = 4n - 22

4n - 2n = 18 + 22

2n = 40

n = 40/2

n = 20

AD = 2(20) + 18

= 40 + 18

AD = 58

Now,

1) Length of AC

AC = 2AD

Here, AD = 58

AC = 2(58)

AC = 116

Hence, The value of AC is 116

2) A is an angle bisector

∠BAE = ∠DAE = 37°

∠DAE = 37°

Δ ADE is a right angle triangle

∠DEA = 90 - ∠DAE

= 90 - 37

= 53°

Since, ∠DEA = ∠BEF

∠BEF = 53°

Hence, The measure of ∠BEF = 53°

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Darell made a scale drawing of a shopping center. The parking lot is 4 centimeters wide in the drawing. The actual parking lot is 40 meters wide. What scale did Darell use?

Answers

Answer:

1 cm to 10 m

Step-by-step explanation:

4 cm to 40 m = 1 cm to 10 m

The following table shows a company's annual income over a 6-year period. The equation y=60000(1.2)x describes the curve of best fit for the company's annual income (y). Let x represent the number of years since 2001.

Answers

Given that the annual income of a company over a 6-year period is described by the equation:

[tex]\begin{gathered} y=60000(1.2)^x \\ \text{where} \\ x\text{ is the number of years since 2001} \end{gathered}[/tex]

The annual income at the end of each year since 2001 is as shown in the table below:

Required: To evaluate the company's approximate annual income in 2009.

Solution:

Given the annual income described as

[tex]y=60000(1.2)^x[/tex]

The number of years between 2001 and 2009 is evaluated as

[tex]x\text{ = 2009 -2001 = 8 years}[/tex]

thus, it's been 8 years since 2001.

The annual income in 2009 is thus evaluated by substituting 8 for the value of x in the annual income function.

This gives

[tex]\begin{gathered} y=60000(1.2)^x \\ x\text{ = 8} \\ \text{thus,} \\ y\text{ = 60000}\times(1.2)^8 \\ =\text{ 60000}\times4.29981696 \\ y=\text{ }257989.0176 \\ \Rightarrow y\approx258000 \end{gathered}[/tex]

Hence, the company's approximate annual income in the year 2009 will be $ 258000.

The third option is the correct answer.

Use the substitution u = (2x - 2) to evaluate the integral x³e(^2x^4-2) dx

Answers

The substitution u = (2x - 2) to the integral x³e(^2x^4-2) dx is (2x – 2)/4 +c

What is meant by integral?In mathematics, an integral assigns numerical values to functions in order to describe concepts like displacement, area, volume, and other outcomes of the combination of infinitesimally small data. Integral discovery is a process that is referred to as integration. One of the fundamental, crucial operations of calculus, along with differentiation, is integration[a]. It can be used to solve issues in mathematics and physics involving, among other things, the volume of a solid, the length of a curve, and the area of an arbitrary shape. The integrals listed here are those that fall under the category of definite integrals, which can be thought of as the signed area of the region in the plane that is enclosed by the graph of a particular function between two points on the real line.

Therefore,

Use the substitution

U = (2x -2)

to evaluate integral x³e(^2x^4-2) dx

let u = 2x -2

du = x dx or dx =du/2

u = 2x-2

du = d(2x – 2)

du = 2dx

dx = du/2

∫ (2x -2)dx = ∫u du/2

=1/2 ∫u du

= ½ u square /2 +c

= u square /4 +c

= (2x – 2)/4 +c

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Find the common ratio of the geometric sequence 19, -76,304, ...

Answers

[tex]a_n=(-4)^{n+1}\cdot k[/tex]

number one name three collinear points number to name four coplanar Point number three name two sets of lines intersect number for name two points not contained in the plane

Answers

The points lying on a single line are called colinear points. So here,

KJD are colinear points as they are lying on a same line.

Points lying on the same plane are called coplanar points. So here, IJFE are coplanar points.

The two sets of line intesects are KD and CF, IG and FH.

The two points that are not in the plane are A and B.

the Center is (2,0) the circle passes through the point (4.5,0) What is the Radius?

Answers

The radius of the circumference would be

x2 = 4.5

x1 = 2

r = x2 - x1

r = 4.5 - 2.0

r = 2.5

The radius would be 2.5

[tex]f(x) = (x - 2) ^{2}(x + 3)(x + 1)^{2} [/tex]the multiplicity of the root x=2 is...?

Answers

The solution of the factor with power 2 in the function f(x) can be found as:

(x-2)=0

x=2.

So, the root is x=2.

The multiplicity is the power of the factor (x-2) with its root given as x=2.

So, the multiplicity of the root x=2 is 2.

Calculate the determinant of this 2x2 matrix. Provide the numerical answer. |2 -1 | |4 -5|

Answers

Given the matrix

[tex]\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}{}\end{bmatrix}[/tex]

its determinant is computed as follows:

ad - cb

In this case, the matrix is

[tex]\begin{bmatrix}{2} & {-1} & \\ {4} & -5 & {}\end{bmatrix}[/tex]

and its determinant is

2(-5) - 4(-1) = -10 - (-4) = -10 + 4 = -6

Knowledge CheckUse the distributive property to remove the parentheses.--7(-5w+x-3)X 5

Answers

Explanation

The distributive property states that:

[tex]k\cdot\left(a+b+c\right?=k\cdot a+k\cdot b+k\cdot c.[/tex]

In this problem, we have the expression:

[tex]-7\cdot(-5w+x-3)=(-7)\cdot(-5w+x-3).[/tex]

Comparing this expression with the general expression of the distributive property, we identify:

• k = (-7),

• a = -5w,

• b = x,

• c = -3.

Using the general expression for the distributive property with these values, we have:

[tex]\left(-7\right)\cdot(-5w)+\left(-7\right)\cdot x+\left(-7\right)\cdot(-3).[/tex]

Simplifying the last expression, we get:

[tex]35w-7x+21.[/tex]Answer

Applying the distributive property to eliminate the parenthesis we get:

[tex]35w-7x+21[/tex]

The numerator of a certain fraction is five times the denominator. If nine is added to both the numerator and the denominator, the resulting fraction is equivalent to two. What was the original fraction (not written in lowest terms)?

Answers

Explanation

To solve the question,

Let

The numerator = x

The denominator = y

So that the original equation will be

[tex]\frac{x}{y}[/tex]

Next, we are told that the numerator is five times the denominator.

So that

[tex]x=5y[/tex]

Again, we are told that If nine is added to both the numerator and the denominator, the resulting fraction is equivalent to two. so

[tex]\frac{x+9}{y+9}=2[/tex]

Hence

we can substitute x =5y into the above

[tex]\begin{gathered} \frac{5y+9}{y+9}=2 \\ \\ cross\text{ multiplying} \end{gathered}[/tex][tex]\begin{gathered} 5y+9=2(y+9) \\ 5y+9=2y+18 \\ Taking\text{ like terms} \\ 5y-2y=18-9 \\ 3y=9 \\ \\ y=\frac{9}{3} \\ \\ y=3 \end{gathered}[/tex]

Thus, the denominator is 3

The numerator will be

[tex]\begin{gathered} x=5y \\ x=5\times3 \\ x=15 \end{gathered}[/tex]

The numerator is 15

Therefore, the fraction is

[tex]undefined[/tex]

factor the trinomial6x² + 17x + 12

Answers

Answer: The factor of the above function is (2x + 3) (3x + 4)

We are given the below function

[tex]6x^2\text{ + 17x + 12}[/tex]

This function can be factor using factorization method

The co-efficient of x^2 = 6

Multiply 6 by 12 to get the constant of the function

12 x 6 = 72

Next, find the factors of 72

Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24

The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9

The new equation becomes

[tex]\begin{gathered} 6x^2\text{ + 17x + 12} \\ 6x^2\text{ + 8x + 9x + 12} \\ \text{Factor out 2}x \\ 2x(3x\text{ + 4) + 3(3x + 4)} \\ (2x\text{ + 3) (3x + 4)} \end{gathered}[/tex]

The factor of the above function is (2x + 3) (3x + 4)

Evaluate: sin-¹(1)
A) 0
B) pi/3
C)pi/2

Answers

A 0 I think It a because it is evaluated to sin-1

Answer:

The correct answer is C. Pi/2

Step-by-step explanation:

I got it wrong on edgen, and it told me the correct answer was C.

Suppose that $16,065 is invested at an interest rate of 6.6% per year, compounded continuously. a) Find the exponential function that describes the amount in the account after time t, in years. b) What is the balance after 1 year? 2 years?5 years? 10 years? c) What is the doubling time?

Answers

Okay, here we have this:

Considering the provided information we obtain the following:

Replacing in the Compound Interest formula we obtain the following:

[tex]\begin{gathered} A(t)=Pe^{rt} \\ A(t)=16065e^{0.066t} \end{gathered}[/tex]

After 1 year (t=1):

[tex]\begin{gathered} A(1)=16065e^{0.066(1)} \\ A(1)\approx17,161.06 \end{gathered}[/tex]

We obtain that after one year the balance is aproximately $17,161.06.

After 2 years (t=2):

[tex]\begin{gathered} A(2)=16065e^{0.066(2)} \\ A(2)=18331.90 \end{gathered}[/tex]

We obtain that after two years the balance is aproximately $18,331.90

After 5 years (t=5):

[tex]\begin{gathered} A(5)=16065e^{0.066(5)} \\ A(5)=$22,345.90$ \end{gathered}[/tex]

We obtain that after five years the balance is aproximately $22,345.90.

After 10 years (t=10):

[tex]\begin{gathered} A(10)=16065e^{0.066(10)} \\ A(10)=$31,082.44$ \end{gathered}[/tex]

We obtain that after ten years the balance is aproximately $31,082.44.

In this case the doubling time will be when she has double what she initially had, that is: $16,065*2=$32130, replacing in the formula:

[tex]32130=16065e^{0.066t}[/tex]

Let's solve for t:

[tex]\begin{gathered} 32130=16065e^{0.066t} \\ 16065e^{\mleft\{0.066t\mright\}}=32130 \\ \frac{16065e^{0.066t}}{16065}=\frac{32130}{16065} \\ e^{\mleft\{0.066t\mright\}}=2 \\ 0.066t=\ln \mleft(2\mright) \\ t=\frac{\ln\left(2\right)}{0.066} \\ t\approx10.502years \end{gathered}[/tex]

Finally we obtain that the doubling time is approximately 10.502 years or about 10 years 6 months.

I need these answers quickly. If I don't get them by midnight ill cry.

Answers

The answer is the second option, “The tank has 200 gallons in it when Jack opens the valve.”

This is because the y intercept represents how much water is in the tank when the time = 0 minutes, and at 0 minutes Jack hasn’t opened the valve yet and no water has been lost.

The change in the value of a stock is represented by the rational number -5.90 describe in words what this means

Answers

The change in the value of a stock which is represented by the rational number -5.90 means that the stock decreased by 5.90 units.

Whenever we use negative value to describe change, it means that the value of that particular entity that been decreased by that number.

On the contrary, If we are using positive value to describe change, it means that the value of that particular entity that been increased by that number.

For example:- The change in total money possessed by Daniel is $ 50 means there is an increase of $ 50 in the money with Daniel.

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The height of a diver above the water’s surface can be modeled by the function h(t)= –16t^2+ 8t + 48. How long does it take the diver to hit the water? Solve by factoring

Answers

Given the function:

[tex]h(t)=-16t^2+8t+48[/tex]

Where h(t) is the height of the diver above the surface of the water and t is the time.

Let's find how long it takes the diver to hit the water.

When the diver hits the water, the height h(t) = 0.

Now substitute 0 for h(t) and solve for the time t.

We have:

[tex]0=-16t^2+8t+48[/tex]

Rearrange the equation:

[tex]-16t^2+8t+48=0[/tex]

Solve for t.

Let's factor the expression by the left.

Factor 8 out of all terms:

[tex]8(-2t^2+t+6)=0[/tex]

Now, factor by grouping.

Rewrite the middle term as a sum of two terms whose product is the product of the first term and the last term:

[tex]\begin{gathered} 8(-2t^2+4t-3t+6)=0 \\ \end{gathered}[/tex]

Solving further:

[tex]\begin{gathered} 8((-2t^2+4t)(-3t+6))=0 \\ \\ 8(2t(-t+2)+3(-t+2))=0 \\ \\ 8(2t+3)(-t+2)=0 \end{gathered}[/tex]

Hence, we have the factors:

[tex]\begin{gathered} 2t+3=0 \\ -t+2=0 \end{gathered}[/tex]

Solve each factor for t:

[tex]\begin{gathered} 2t+3=0 \\ \text{ Subtract 3 from both sides:} \\ 2t=-3 \\ \text{ Divide both sides by 2:} \\ \frac{2t}{2}=-\frac{3}{2} \\ t=-\frac{3}{2} \\ \\ \\ -t+2=0 \\ t=2 \end{gathered}[/tex]

Hence, we have the solutions:

t = -3/2

t = 2

The time cannot be negative, so let's take the positive value.

Therefore, the will take 2 seconds for the diver to hit the water.

ANSWER:

2 seconds.

Find all solutions to the equationin the interval [O, 27). Enter thesolutions in increasing order.cos 2x = cos X[?]Tx = 0,2Remember: cos 20 = cos20 – sin20

Answers

SOLUTION

From

[tex]\begin{gathered} \cos 2x=\cos x \\ \cos ^2x-\sin ^2x=\cos x \\ \cos ^2x-(1-\cos ^2x)=\cos x \\ 2\cos ^2x-1=\cos x \\ 2\cos ^2x-\cos x-1=0 \\ \text{From the quadratic formula} \\ \cos x=\frac{1\pm\sqrt[]{1-(-8)}}{4} \\ \\ \cos x=\frac{1\pm3}{4} \\ \cos x=\text{ 1 or -}\frac{1}{2} \\ \text{Taking the cos}^{-1}of\text{ 1 and -}\frac{1}{2} \\ We\text{ have }\theta\text{ = 0, }\frac{2\pi}{3},\frac{4\pi}{3},\frac{8\pi}{3}\ldots\ldots\ldots2\pi \end{gathered}[/tex]

So your answer is

[tex]0,\text{ }\frac{2\pi}{3},\text{ }\frac{4\pi}{3}[/tex]

there are 5 adult cats, 6 middle aged cats, and ___ kittens, if there are 19 animals in total, how many kittens are there, solve for the blank.

Answers

ANSWER

There are 8 kittens

EXPLANATION

If the sum of the number of adult cats, middle aged cats and kittens is 19:

[tex]\begin{gathered} \text{adult}+\text{middle aged+kittens=19} \\ 5+6+\text{kittens}=19 \\ \text{kittens}=19-5-6 \\ \text{kittens}=8 \end{gathered}[/tex]

The average score for games played in the NFL is 22 and the standard deviation is 9.3 points. 41 games are randomly selected. Round all answers to 4 decimal places where possible and assume a normal distribution.

a. What is the distribution of ¯x x¯
? ¯xx¯ ~ N( , )
b. What is the distribution of ∑x ? ∑x ~ N ( , )
c. P( ¯x > 19.8214) =
d. Find the 60th percentile for the mean score for this sample size.
e. P(20.6214 < x¯< 23.2262) =
f. Q1 for the x¯distribution =
g. P( ∑x > 829.0774) =

For part c) and e), Is the assumption of normal necessary? NoYes

Answers

Using the normal distribution and the central limit theorem, it is found that:

a) The distribution is: x¯ ~ N(22, 1.45).

b) The distribution is: ∑x ~ N(902, 59.55).

c) P( ¯x > 19.8214) = 0.9332 = 93.32%.

d) The 60th percentile for the mean score for this sample size is of 22.37 points a game.

e) P(20.6214 < x¯< 23.2262) = 0.6312 = 63.12%.

f) Q1 for the x¯distribution = 21 points a game.

g) P( ∑x > 829.0774) = 0.8888 = 88.88%.

Assumption of normality is not necessary, as the sample sizes are greater than 30.

Normal Probability Distribution

The z-score of a measure X of a variable that has mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].Also by the Central Limit Theorem, for the sum of n instances of a variable, the mean is of [tex]\n\mu[/tex] and the standard deviation is of [tex]\sigma\sqrt{n}[/tex].Finally, by the Central Limit Theorem, assumption of normality is only necessary when the sample size is less than 30.

For a single game, the mean and the standard deviation of the number of points scored are given as follows:

[tex]\mu = 22, \sigma = 9.3[/tex]

For the average of 41 games, the standard error is:

[tex]s = \frac{9.3}{\sqrt{41}} = 1.45[/tex]

Hence the distribution is: x¯ ~ N(22, 1.45).

For the sum of the 41 games, the mean and the standard error are given as follows:

41 x 22 = 902.[tex]s = 9.3\sqrt{41} = 59.55[/tex].

Hence the distribution is: ∑x ~ N(902, 59.55).

In item c, the probability is one subtracted by the p-value of Z when X = 19.8214, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem: