The average hourly wage for a high school student in Illinois is $8.25 per hour with a standard deviation of $.25. Assume hourly wages vary normally.
A) Determine the margin of error for this scenario.
B) For the previous question you just answered, construct a 95% confidence interval for the hourly wage for a high school student.
C) For the 95% confidence interval you just constructed, does an hourly wage of $9.15 fall within that acceptable range?

Answers

Answer 1

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: hourly wage of a high school student

X~N(μ;σ²)

X[bar]= $8.25

σ= $0.25

For a 95% CI for the average hourly wage for 1 high school student:

For this exercise you have to consider the sample size n=1

a) The margin of error of the CI is calculated as:

d= [tex]Z_{1-\alpha /2}[/tex] * σ

1-α: 0.95 ⇒ α:0.05

1-α/2:0.975

[tex]Z_{1-\alpha /2}= Z_{0.975}= 1.96[/tex]

d= 1.96 * 0.25= 0.49

b)

The formula for the interval is

X[bar] ± [tex]Z_{1-\alpha /2}[/tex] * σ

[8.25 ± 0.49]

[7.76; 8.74]

With a 95% you'd expect the interval $[7.76; 8.74] to include the average hourly wage of one high school student in Illinois.

c)

Te calculated interval is $ [7.76; 8.74] the value $9.15 does nor fall within that acceptable range.

I hope this helps!


Related Questions

Matt says 3/3 is equivalent to 1 is he correct?

Answers

Answer: Yes

Step-by-step explanation:

It isn't an

1 an improper fraction

Less than the denominator

Therefore, three thirds or 3/3 is one whole fraction

Rly hope I helped!

☆꧁Ashlin꧂☆

Answer:yes he his correct

Step-by-step explanation:

3/3=1

If three points of a parallelogram are A (-5, -2), B (1,5), C (7.1). Which of the
following is the fourth point D of parallelogram ABCD?
(13,8)
(13.-6)
(1. -2)
(1,-6)​

Answers

(1,-6) is the answer

Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters which measurement does 17 meters represent

Answers

The answer in length

The length is used to measure the distance between to end points or edges. so 17 meters measurement represent the length.

What is perimeter?

Its the sum of length of the sides used to made the given figure.

Talia is going to put a new carpet in her house. She measure's one side of her living room and finds it measures 17 meters.

Area is what is on the inside.

The perimeter is the outside of the hole thing.

Hence, the length is used to measure the distance between to end points or edges.

so 17 meters measurement represent the length.

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Who’s good on algebra 1 ? Need help

Answers

Answer:

Which expression is equivalent to 3 over 175

I would say try - C or D

Choose the property of addition. ( 5 + 3 ) + 8 = 5 + ( 3 + ? )

A. associate property of addition
B. Commutative property of addition
C. Distributive property
D. Identity property of addition

Answers

Answer:

A. associative property of addition

Step-by-step explanation:

Associative because you can add or multiply those regardless of how the numbers are grouped.

I hope this helped and have a good rest of your day!

Answer:

Associative Property of Addition

Step-by-step explanation:

This property states that the sum of 3 or more numbers stays the same, no matter how they are grouped.

Hope this helped. Have an awesome day!

Hi guys, Can anyone help me with this tripple integral? Thank you:)

Answers

I don't usually do calculus on Brainly and I'm pretty rusty but this looked interesting.

We have to turn K into the limits of integration on our integrals.

Clearly 0 is the lower limit for all three of x, y and z.

Now we have to incorporate

x+y+z ≤ 1

Let's do the outer integral over x.  It can go the full range from 0 to 1 without violating the constraint.  So the upper limit on the outer integral is 1.

Next integral is over y.  y ≤ 1-x-z.   We haven't worried about z yet; we have to conservatively consider it zero here for the full range of y.  So the upper limit on the middle integration is 1-x, the maximum possible value of y given x.

Similarly the inner integral goes from z=0 to z=1-x-y

We've transformed our integral into the more tractable

[tex]\displaystyle \int_0^1 \int_0^{1-x} \int _0^{1-x-y} (x^2-z^2)dz \; dy \; dx[/tex]

For the inner integral we get to treat x like a constant.

[tex]\displaystyle \int _0^{1-x-y} (x^2-z^2)dz = (x^2z - z^3/3)\bigg|_{z=0}^{z= 1-x-y}=x^2(1-x-y) - (1-x-y)^3/3[/tex]

Let's expand that as a polynomial in y for the next integration,

[tex]= y^3/3 +(x-1) y^2 + (2x+1)y -(2x^3+1)/3[/tex]

The middle integration is

[tex]\displaystyle \int_0^{1-x} ( y^3/3 +(x-1) y^2 + (2x+1)y -(2x^3+1)/3)dy[/tex]

[tex]= y^4/12 + (x-1)y^3/3+ (2x+1)y^2/2- (2x^3+1)y/3 \bigg|_{y=0}^{y=1-x} [/tex]

[tex]= (1-x)^4/12 + (x-1)(1-x)^3/3+ (2x+1)(1-x)^2/2- (2x^3+1)(1-x)/3[/tex]

Expanding, that's

[tex]=\frac{1}{12}(5 x^4 + 16 x^3 - 36 x^2 + 16 x - 1)[/tex]

so our outer integral is

[tex]\displaystyle \int_0^1 \frac{1}{12}(5 x^4 + 16 x^3 - 36 x^2 + 16 x - 1) dx[/tex]

That one's easy enough that we can skip some steps; we'll integrate and plug in x=1 at the same time for our answer (the x=0 part doesn't contribute).

[tex]= (5/5 + 16/4 - 36/3 + 16/2 - 1)/12[/tex]

[tex]=0[/tex]

That's a surprise. You might want to check it.

Answer: 0

−7×8=?????????????????????????

Answers

Answer

the answer is -56

Step-by-step explanation:

If the mean of a symmetric distribution is 60, which of these values could be
the median of the distribution?
A. 100
B. 60
C. 80 As
D. 30
SUBMIT

Answers

Answer:

i think ...

Step-by-step explanation:

symmetric distribution  usually be a bell shape distribution .

most likely the median = mean = 60

The required value of 60 could be the median of the distribution. Option B is correct.

What is mean?

The mean of the values is the ratio of the total sum of values to the number of values.

What is the median?

When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top 50% of data.

Here,
The mean of a symmetric distribution is 60.
Since for the symmetric data and rational data, the mean is equal to the median,
So Mean = Median
Median = 60

Thus, the required value of 60 could be the median of the distribution.

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Graph the equation y=x²-8x+7 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.

Answers

Answer:

vertex is: (4,-9)

y intercept= (0,7)

roots= (1,0) and (7,0)

Step-by-step explanation:

so we can use factoring to solve this quadratic equation real quick:

x^2-7x-1x+7

x(x-7)

-1(x-7)

(x-1)(x-7)=0

x-1=0

x=1

x-7=0

x=7

(1,0) and (7,0) are the roots

axis of symmetry: 8/2=4

substitute axsis of symmetry in equation to get vertex:

4^2-8(4)+7

16-32+7

-16+7=-9

vertex is: (4,-9)

y intercept= (0,7)

roots= (1,0) and (7,0)

Hope this helps

Write the fraction from least to greatest: 1/8, 1/3, 1/8

Answers

Answer:

Start with making them equal.

1/8 --> 3/24

1/8 --> 3/24

1/3 --> 8/24

Now order them.

1/8, 1/8, 1/3.

Hope this helps ;)

If the fish tanks dimension are 60 by 15 by 34 and its is completely empty, what volume of water is needed to fill three fourths of the aquarium? Please help

Answers

Answer:

22,950 units³

Step-by-step explanation:

All you have to do is:

[tex]\frac{3}{4} *60*15*34=\\45*15*34=\\675*34=\\\\22,950[/tex]

Choose the equation that best fits the following graph.​

Answers

Answer:

  c.  y = 3.25^x

Step-by-step explanation:

At x=1, the value of y is slightly more than 3, so the base must be more than 3. The appropriate choice is ...

  y = 3.25^x

Ming throws a stone off a bridge into a river below.
The stone's height (in meters above the water), xxx seconds after Ming threw it, is modeled by:
h(x)=-5(x-1)^2+45h(x)=−5(x−1)
2
+45h, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, minus, 1, right parenthesis, squared, plus, 45
How many seconds after being thrown will the stone reach its maximum height?

Answers

Answer:

1 seconds after being thrown, the stone reaches its max height

Step-by-step explanation:

Answer:1 Seconds Is wrong the correct answer is 2

Step-by-step explanation:

Khan said so

PLEASE LIKE AND RATE IF YOU GOT YOUR QUESTION RIGHT!!!

3A wholesaler buys baseball gloves for $15 each. He then marks up the price to $20. By what percentage was the price of the baseball glove increased

Answers

Answer:

25%

Step-by-step explanation:

Which of the following values of n will result in a true statement when substituted into the given equation? 4n + 9 = 1 A. n = -2 B. n = 2 C. n = 3 D. n = 4

Answers

Answer:

A. n = -2

Step-by-step explanation:

A. n = -2

4(-2) + 9 = 1

-8 + 9 = 1

1 = 1

The value of n for which the statement of equation 4n + 9 = 1 holds true is n = -2.

Given an equation:

4n + 9 = 1

There are some given options for the value of n.

It is required to find the value of n, where the statement is true.

A) When n = -2:

4n + 9 = 4(-2) + 9

          = 1

B) When n = 2:

4n + 9 = 4(2) + 9

          = 17

C) When n = 3:

4n + 9 = 4(3) + 9

          = 21

D) When n = 4:

4n + 9 = 4(4) + 9

          = 25

Hence the true statement is when n = -2.

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Sheila earns $8 per hour at her afterschool job. After working one week, she received a paycheck for $104. Write and solve an equation to find the number of hours Sheila worked. Fill in the blank with the solution only.

Answers

Answer:

13

Step-by-step explanation:

It should just be 104 divided by 8 which equals=13

Determine the value of x for the triangle. show work.

Answers

Answer:

x=5

Step-by-step explanation:

x, x+7, x+8 must be a Pythagorean triple for it to make a right triangle. The only Pythagorean triple fitting these numbers is 5, 12, 13 so x must be 5.

Answer:

5

Step-by-step explanation:

Because this is a right triangle, you know that by the Pythagorean theorem:[tex]\sqrt{(x+7)^2+x^2}=x+8[/tex]

Squaring both sides to get rid of the square root:

[tex](x+7)^2+x^2=(x+8)^2[/tex]

Expanding all of the parentheses:

[tex]x^2+14x+49+x^2=x^2+16x+64[/tex]

Combine like terms:

[tex]x^2-2x-15=0[/tex]

Factor:

[tex](x-5)(x+3)=0[/tex]

Since x cannot be negative, it is equal to 5. Hope this helps!

In ΔPQR, the measure of ∠R=90°, RP = 9.9 feet, and QR = 3.2 feet. Find the measure of ∠P to the nearest tenth of a degree.

Answers

Answer:

17.9

Step-by-step explanation:

profit 75% retail $350. what is cost at wholesale

Answers

Answer:

Step-by-step explanation:

350-75%=87.5\\so 350-87.5\\=262.5\\$262.5 dolla profit\\

Which of the following is not a binorrial experiment?
a Asking 100 people whether or not the like pizza.
b. Measuring the height of 100 people to see if they are over 61.
Asking 100 people what their favorite color is.
d. Asking 100 people if their favorite color is red.

Answers

Answer:

You don't need experiments to ask people questions

Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material. One study of resprouting took place in a dry area of Mexico. The investigation clipped the tops of samples of several species of shrubs. In some cases, they also applied a propane torch to the stumps to simulate a fire. Of 19 specimens of a particular species, 6 resprouted after fire. Estimate with 96% confidence the proportion of all shrubs of this species that will resprout after fire. Interval: .1884 to

Answers

The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.

Here, we have,

To estimate the proportion of all shrubs of this species that will resprout after fire with 96% confidence, we will use the formula for a confidence interval for a proportion.

The formula for the confidence interval for a proportion (p) is given by:

CI = p ± Z * √(p * (1 - p) / n)

where:

CI is the confidence interval

p is the sample proportion (resprouted specimens / total specimens)

Z is the critical Z-score corresponding to the desired confidence level (96% confidence level corresponds to a Z-score of approximately 1.750)

n is the sample size (total number of specimens)

Given information:

Total number of specimens (n) = 19

Number of specimens that resprouted after fire = 6

Now, calculate the sample proportion (p):

p = (number of specimens that resprouted) / (total number of specimens)

p = 6 / 19 ≈ 0.3158 (rounded to four decimal places)

Now, calculate the critical Z-score for a 96% confidence level (use a Z-table or calculator):

Z ≈ 1.750

Now, calculate the margin of error (E):

E = Z * √(p * (1 - p) / n)

E = 1.750 * √(0.3158 * (1 - 0.3158) / 19)

E ≈ 0.1884 (rounded to four decimal places)

Finally, calculate the confidence interval:

CI = p ± E

CI = 0.3158 ± 0.1884

The 96% confidence interval for the proportion of all shrubs of this species that will resprout after fire is approximately 0.1274 to 0.5042.

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Write an equation of the line passing through the point A(2, 0) that is parallel to the line y = 3x−5

Answers

Answer:

y = 3x-6

Step-by-step explanation:

y = 3x−5

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

m =3

Parallel lines have the same slope

We have the slope m=3 and a point (2,0)

y = mx+b

y = 3x+b

Substituting the point into the equation to solve for b

0 = 3(2)+b

0 = 6+b

b = -6

y = 3x-6

Answer:

y = 3x - 6

Step-by-step explanation:

Parallel lines have the same slope,

So m = 3

y - 0 = 3(x - 2)

y = 3x - 6

Show steps how to solve for y!!!!!
2y+2=3y/2
Please help me

Answers

[tex]\text{Solve for y:}\\\\2y+2=\frac{3y}{2}\\\\\text{Multiply both sides by 2 to cancel the denominator}\\\\4y+4=3y\\\\\text{Subtract 3y from both sides}\\\\y+4=0\\\\\text{Subtract 4 from both sides}\\\\\boxed{y=-4}[/tex]

Answer:-4

Step-by-step explanation:

2y+2=3y/2

Cross multiply

2(2y+2)=3y

Open bracket

4y+4=3y

Collect like terms

4y-3y=-4

y=-4

if 8% is deducted from the bill,$384 bill remains to be paid. How much is the original bill?

Answers

Answer:

$353.28

Step-by-step explanation:

The senior classes at Snellville High and General High planned separate trips to the water park. The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students. General High rented and filled 14 vans and 12 buses with 738 students. How many students would fill 2 buses and 3 vans?

Answers

Answer:

133 Students

Step-by-step explanation:

Let the number of student in a van=v

Let the number of student in a bus=b

The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students.

Therefore: 12v+14b=796

General High rented and filled 14 vans and 12 buses with 738 students.

Therefore: 14v+12b=738

We solve the two resulting equations simultaneously

12v+14b=796

14v+12b=738

Multiply equation 1 by 12 and equation 2 by 14 to eliminate b

144v+168b=9552

196v+168b=10332

Subtract

-52v=-780

Divide both sides by -52

v=15

We substitute v=15 to obtain b in any of the equations

12v+14b=796

12(15)+14b=796

14b=796-180

14b=616

Divide both sides by 14

b=44

Therefore a bus contains 44 Students and a Van contains 15 students.

Number of Students who would fill 2 buses and 3 vans

=2b+3v

=2(44)+3(15)

=133 Students

What type of lines are shown?​

Answers

Answer:

the angle is acute angle

Answer:

The type of angle shown is an acute angle

Step-by-step explanation:

there are 4 main types of angles. this is an acute angle as it is less than 90°.

Types of angles:

The 4 main types of angles are: acute, obtuse, right angles, reflex angles.

Acute angles- Acute angles are angles less than 90°.

Obtuse Angles-Obtuse angles are angles greater than 90° but less than 180°.

Right Angles- Right angles are angles of 90°.

Reflex Angles- Reflex angles are angles greater than 180° but less than 360°.

The MIT soccer team has 2 games scheduled for one weekend. It has a 0.4 probability of not losing the first game. and a 0.7 probability of not losing the second game, independent of the first. If it does not lose a particular game, the team is equally likely to win or tie. independent of what happens in the other game. The MIT team will receive 2 points for a win, 1 for a tie. and 0 for a loss. Find the PMF of the number of points that the team earns over the weekend.

Answers

Answer:

Step-by-step explanation:

To determine the PMF of the points that the team receive, we must determine the probabilities of winning each of the games.

Consider the firt game. We know that the probability of not losing is 0.4. Since the team can either lose the game or not, we have that the probability of losing it is 0.6. We are told that given that the team does not lose, the probability of winning or having a tie is the same. Recall that, given events A, B, the conditional probability P(A|B) (which means probability of A given B) is given as

[tex]P(A|B) = \frac{P(A\cap B)}{P(B)}[/tex]

in our case, we have that B:= not losing the game. Consider A:= To win the game, C:= To tie the game. We know that P(A|B)=P(C|B). When the team doesn't lose, then the team either ties or wins, this means that

[tex]P(A|B)+P(C|B) = 1[/tex]

So we get that P(A|B) = P(C|B) = 1/2. Let us find P(A)

[tex]P(A|B) = \frac{P(A\cap B)}{P(B)} = \frac{P(A)}{P(B)}=\frac{1}{2}[/tex]

Then [tex]P(A) = \frac{P(B)}{2} = 0.2[/tex]. By an analogous calculation we have that P(A) = P(C) = 0.2.

We will define the following events: [tex]W_i[/tex] is the event that the team wins the game i, [tex]T_i[/tex] is the event that the team ties the game i and [tex]L_i[/tex] is the event that the team loses the game i. In this notation, we have that

[tex]P(W_1) = P(T_1) = 0.2, P(L_1) = 0.6[/tex]

By reasoning the same way for the second game, we can calculate that

[tex]P(W_2)=P(T_2)=0.35, P(L_2) = 0.3[/tex]

To calculate the PMF we must check all the possible outcomes of the results of both games. Since we can either win (W), tie(T) or lose(L) a game, we will express the outcome as follows TW(3) means that the team ties  the first game and wins the second one, for a total of points. In this way, the possible outcomes are

WW(4), WT(3), WL(2), TW(3), TT(2), TL(1), LW(2), LT(1), LL(0)

We see that the number of possible points are 0,1,2,3,4. Let X be the number of points, to get the pmf of X is to give the probability P(X=k) for k=0,1,2,3,4 explicitly. Note that since each game is independent of each other, to get the probability of one of the outcomes it suffices to multiply the probability of each event. For example we have that [tex]P(WW) = P(W_1)\cdotP(W_2) = 0.07[/tex]

Then, the pmf is given by

[tex]P(X=0) = P(LL) = 0.18[/tex]

[tex]P(X=1)=P(LT)+P(TL) = 0.27[/tex]

[tex]P(X=2)=P(LW)+P(TT)+P(WL) = 0.34[/tex]

[tex]P(X=3)=P(WT)+P(TW) = 0.14[/tex]

[tex]P(X=4)=P(WW)= 0.07[/tex]

Which category is not one of the major responsibilities of state government?
A. Economic development
B. Corrections
C. Electrical power
D. Law enforcement

Answers

Answer: C electricity

Step-by-step explanation:

It is

C. electrical power

A movie theater has a seating capacity of 387. The theater charges $5.00 for children, $7.00 for students, and $12.00 of
adults. There are half as many adults as there are children. If the total ticket sales was $ 2808, How many children,
students, and adults attended?

Answers

Answer:

The attendance was 198 children, 90 students and 99 adults.

Step-by-step explanation:

We define:

c: children attendance

s: students attendance

a: adult attendance

The equation that describes the total ticket sales is:

[tex]5c+7s+12a=2808[/tex]

We also know that the children attendance doubles the adult attendance:

[tex]c=2a[/tex]

The third equation is the seating capacity, which we assume is full:

[tex]c+s+a=387[/tex]

We start by replacing variables in two of the equations:

[tex]c=2a\\\\s=387-c-a=387-2a-a=387-3a[/tex]

Then, we solve the remaining equation for a:

[tex]5c+7s+12a=2808\\\\5(2a)+7(387-3a)+12a=2808\\\\10a+(2709-21a)+12a=2808\\\\10a+12a-21a=2808-2709\\\\a=99[/tex]

Then, we solve for the other two equations:

[tex]c=2a=2*99=198\\\\s=387-3a=387-3*99=387-297=90[/tex]

The attendance was 198 children, 90 students and 99 adults.

3.6 x 0.025 is my question to be answered

Answers

Answer:

0.09

because I multiplied...

Answer:

0.09

Step-by-step explanation:

36/ 10 x 25/ 1000 = 18/ 5 x 1/40 = 9/100 = 0.09

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