Estimating Mean SAT Math Score
Type numbers in the boxes.
aby Part 1: 5 points
The SAT is the most widely used college admission exam. (Most community
aby Part 2: 5 points
colleges do not require students to take this exam.) The mean SAT math score
varies by state and by year, so the value of u depends on the state and the year. 10 points
But let's assume that the shape and spread of the distribution of individual SAT math scores in each
state is the same each year. More specifically, assume that individual SAT math scores consistently
have a normal distribution with a standard deviation of 100. An educational researcher wants to
estimate the mean SAT math score (u) for his state this year. The researcher chooses a random
sample of 661 exams in his state. The sample mean for the test is 494.
Find the 99% confidence interval to estimate the mean SAT math score in this state for this year.
(Note: The critical z-value to use, zc, is: 2.576.)
Your answer should be rounded to 3 decimal places.

Answers

Answer 1

Answer:

(483.981 ; 504.019)

Step-by-step explanation:

Given :

σ = 100

Sample size, n = 661

xbar = 494

We use the Z distribution since we are working with the population standard deviation ;

C.I = xbar ± (Zcritical * σ/√n)

Zcritical at 99% = 2.576

C.I = 494 ± (2.576 * 100/√661)

C.I = 494 ± 10.019

Lower boundary = (494−10.019) = 483.981

Upper boundary = (494+10.019) = 504.019

C.I = (483.981 ; 504.019)


Related Questions

Which of the following has the least value?

30% of 50
O 50% of 30
30% of 30
50% of 50

Answers

Answer:

30% of 30 has the least value out of all answer choices.

Step-by-step explanation:

Solve for the values of the given percentages of each number:

30% of 50:

Divide 50 by 100 to get 1%

50/100 = 0.5

Multiply 1% (0.5) by 50:

0.5 x 50 = 15

So 30% of 50 = 15

50 % of 30:

50% of a number means half of it since 50% is half of 100% so:

30/2 = 15

So 50% of 30 = 15

30% of 30:

Divide 30 by 100 to get 1%:

30/100 = 0.3

Multiply 1% (0.3) by 30:

0.3 x 30 = 9

So 30% of 30 = 9

50% of 50

50% of a number means half of it since 50% is half of 100% so:

50/2 = 25

So 50% of 50 = 25

Let’s arrange all of the values from greatest to least (left to right) to determine the most least value:

25, 15, 15, 9

9 is the most least, it is the value equal to the answer choice “30% of 30”

HOPE THIS HELPED!

In a 2-digit number, the tens digit is 5 less than the units digit. If you reverse the number, the result is 7 greater than double the original number. Find the original number.

Answers

The original number is 38

A 2-digit number can be written as:

N = a*10 + b*1

Where a is the tens digit, and b is the units digit, these two are single-digit numbers.

We know that:

"the tens digit is 5 less than the units digit."

This means that:

a = b - 5

(notice that a must be larger than zero and smaller than 10, from this, we can conclude that b is a number in the range {6, 7, 8, 9})

"If you reverse the number, the result is 7 greater than double the original number"

The reverse number is:

b*10 + a

and this is 7 greater than 2 times the original number, then:

b*10 + a = 7 + 2*(a*10 + b)

Then we found two equations:

a = b - 5

b*10 + a = 7 + 2*(a*10 + b)

Replacing the first equation in the second, we get:

b*10 + (b - 5) = 7 + 2*((b - 5)*10 + b)

Now let's solve that:

b*10 + b - 5 = 7 + 2*(11*b - 50)

11*b - 5 = 7 + 22*b - 100

-5 - 7 + 100 = 22*b - 11*b

88 = 11*b

88/11 = b = 8

Now that we know that b = 8, we can use the equation:

a= b - 5

a = 8 -5 = 3

Then the original number is:

a*10 +  b = 3*10 + 8 = 38

The original number is 38

If you want to read more about this, you can see:

https://brainly.com/question/19902993

What is the slope of a line perpendicular to line A?

Answers

Vas happenin
Hope your day is going well
The slope equation is y2- y1/ x2-x1
Y2 = 5
Y1 = 0
X2= 3
X1= -7
5-0/ 3 - -7
5/10 5 divided by 10 is 2
Your slope is 2
Hope this helps *smiles*

½ sejam berapa minit?​

Answers

Answer:

1/2 jam 30 menit mungkin?

1/2 jam adalah 30 minit

1/2 × 60 = 30 mins

English translation

1/2 an hour is 30 minutes

1/2 × 60 = 30 mins

Answered by Gauthmath must click thanks and mark brainliest

Please help out explanation need it

Answers

Answer:

[tex] \sin(θ) = \frac{19}{41} \\ θ = 27.6 \\ θ = 28[/tex]

You have $90 in your bank account. Each work you plan to deposit $3 from your allowance and $25 from your paycheck. The equation b: 90+ (25+5)w gives the amount b in your account after w woeks. How rary works from
now will you have $220 in your bank account?
There will be 5220 in the account after works
(Type a whole number

Answers

90+(25+8)W=220
33w=220-90
33w=130 /33
W = 3.94

2. Solve the following system of equations. y = 5 + x 2x + 2y = 30

Answers

x = 5

since we know y= 5 + x , plug this into y in the second equation.

2x + 2 (5 + x) = 30

distribute 2 into the 5 and x

2x + 10 + 2x = 30

combine like terms

4x + 10 = 30

subtract 10 from both sides

4x = 20

divide four by both sides to isolate the variable

x = 5
Answer is d 1+2 y=5 add all cards

9sin(Θ)-7=0. Solve the trigonometric equation

Answers

Step-by-step explanation:

here's the answer to your question

Primo car rental agency charges $21 per day plus $0.20 por milo. Ultimo car rental agency charges $24 per day plus $1.00 per milo. Find the daily mileage for which the Ultimo charge is four times the Primo charge.
The mileage is

Answers

Answer:

300 miles

Step-by-step explanation:

Let us consider the miles they travelled is 'm'

Mileage for Primo= 21 + (m × 0.20) = 21+0.2m

Mileage for Ultimo= 24+ ( m× 1.00) = 24 + m

Question says The mileage is equal when Ultimo's charge is 4× Primo

Thus,

4 × (21+0.2m) = 24+ m

84 + 0.8m = 24 + m

60 = 0.2m

m = 300

PLEASE ANSWER
Triangle ABC is similar to triangle DEF. find the length of median CP
A. 12
B. 16
C. 24
D.48​

Answers

12/16 = (3x-12)/(2x+8)

16(3x-12)=12(2x+8)

48x-192=24x+96

48x-24x=192+96

24x=288

X=288/24

X=12

3x-12

=(12x3)-12

=36-12

=24

C is the answer

Hope this helps!

Answer:

48

Step-by-step explanation:

2x+8=3x-12(ABCP ~FDQE)

2x-3x= -8-12

-x= -20

x=20

now,

CP=3x-12

3*20-12

48

A bicyclist is at point A on a paved road and must ride to point C on another paved road. The two roads meet at
an angle of 38° at point B. The distance from A to B is 18 mi, and the distance from B to C is 12 mi (see
the figure). If the bicyclist can ride 22 mph on the paved roads and 6.8 mph off-road, would it be faster for the bicyclist to ride from A to C on the paved roads or to ride a direct line from A to C off-road? Explain.

Answers

Answer:

Step-by-step explanation:

The diagrammatic expression to understand this question very well is attached in the image below.

By applying the law of cosine rule; we have:

a² = b² + c² - 2bc Cos A --- (1)b² = a² + c² - 2ac Cos B --- (2)c² = a² + b² - 2ab Cos C --- (3)

From the diagram attached below, we need to determine the side "b" by using equation (2) from above:

b² = a² + c² - 2ac Cos B

From the information given:

a = 12 miles;  c = 18 miles;   ∠B = 38°

replacing the values into the above equation:

b² = 12² + 18² - 2(12)(18) Cos (38°)

b² = 144 + 324 - 432 × (0.7880)

b² = 468 - 340.416

b² = 127.584

[tex]b = \sqrt{127.584}[/tex]

b = 11.30 miles

However, we are also being told that the speed from A → C = 6.8 mph

Thus, the time required to go from A → C  can be determined by using the relation:

[tex]\mathbf{speed = \dfrac{distance}{time}}[/tex]

making time the subject of the formula, we have:

[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]

[tex]\mathbf{time= \dfrac{11.30}{6.8}}[/tex]

time = 1.66 hours

By using the paved roads, the speed is given as = 22 mph

thus, the total distance covered = |AB| + |BC|

= (18+12) miles

= 30 miles

[tex]\mathbf{time= \dfrac{distance}{speed }}[/tex]

[tex]\mathbf{time= \dfrac{30}{22}}[/tex]

time = 1.36 hours

Therefore, the time used off-road = 1.661 hours while the time used on the paved road is 1.36 hours.

Since we are considering the shortest time possible;

We can conclude that it would be faster for the bicyclist to ride from A to C on the paved roads since it takes a shorter time to reach its destination compared to the time used off-road.

Learn more about Law of cosine here:

https://brainly.com/question/24077856?referrer=searchResults

It would be faster for the bicyclist to ride from A to C on the paved roads since the time to go from A to C on the paved roads is 1.4 h and the time to go from A to C off-road is 1.7 h.        

To calculate which way would be faster we need to find the distance from point A to C with the law of cosines:

[tex] \overline{AC}^{2} = \overline{AB}^{2} + \overline{BC}^{2} - 2\overline{AB}\overline{BC}cos(38) [/tex]

Where:

[tex]\overline{AB}[/tex]: is the distance between the point A and B = 18 mi

[tex]\overline{BC}[/tex]: is the distance between the point B and C = 12 mi        

[tex] \overline{AC} = \sqrt{(18 mi)^{2} + (12 mi)^{2} - 2*18 mi*12 mi*cos(38)} = 11.3 mi [/tex]

Now, let's find the time for the two following cases.

1. From point A to C on the paved roads (t₁)

[tex] t_{1} = t_{AB} + t_{BC} [/tex]

The time can be calculated with the following equation:

[tex] t = \frac{d}{v} [/tex]    (1)

Where:

d: is the distance

v: is the velocity

Then, the total time that it takes the bicyclist to go from point A to C on the paved roads is:

[tex] t_{1} = t_{AB} + t_{BC} = \frac{18 mi}{22 mph} + \frac{12 mi}{22 mph} = 1.4 h = 84 min [/tex]

2. From point A to C off-road (t₂)

With equation (1) we can calculate the time to go from point A to C off-road:

[tex] t_{2} = \frac{\overline{AC}}{v_{2}} = \frac{11.3 mi}{6.8 mph} = 1.7 h = 102 min [/tex]

Therefore, it would be faster for the bicyclist to ride from A to C on the paved roads.  

To find more about the law of cosines, go here: https://brainly.com/question/15740431?referrer=searchResults  

I hope it helps you!                                  

look at the image below

Answers

Answer:

201.1 km²

Step-by-step explanation:

Surface area of the figure,

4πr²

= 4×π×4²

= 64π

= 201.1 km² (rounded to the nearest tenth)

Salaries of entry-level computer engineers have Normal distribution with unknown mean and variance. Three randomly selected computer engineers have following salaries (in $1000s): 70, 80, 90. The average and the standard deviation of the data in the sample are 80 and 10. Using hypothesis testing, determine if this sample provides a sufficient evidence, at a 10% level of significance, that the average salary of all entry-level computer engineers is different from $60,000.
a. Null hypothesis.
b. alternative hypothesis.
c. test statistic.
d. acceptance region.

Answers

Answer:

H0 : μ = 60000

H1 : μ ≠ 60000

Test statistic = 3.464

Step-by-step explanation:

Given :

Sample mean salary, xbar = 80000

Sample standard deviation, s = 10000

Population mean salary , μ = 60000

Sample size, n = 3

Hypothesis :

H0 : μ = 60000

H1 : μ ≠ 60000

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (80000 - 60000) ÷ (10000/√(3))

T = 20000 / 5773.5026

T = 3.464

The Decison region :

If Tstatistic >Tcritical

Tcritical at 10%, df = 2 ; two - tailed = 2.9199

Tstatistic > Tcritical ; He

Which could be a binomial expansion of (4x + y)?
16x2 + xy + y2
16x2 + 4xy + y2
O 64x3 + 16x2y + 5xy2 + y3
64x3 + 48x2y + 12xy2 + y3
+

Answers

Answer: D

Step-by-step explanation:

[tex](4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D[/tex]

Answer:

D

Step-by-step explanation:

Sydney has finished all his work on time, but many of his teammates are still struggling to complete their assignments. What should he do? a) Not distract them; they may get farther behind. O b) Listen to them complain about their workloads O c) Help them complete their work d) Share his thoughts on how they could get their work done faster

Answers

Answer:

I think the correct option is c

Answer:

I think the correct answer is (d)

Step-by-step explanation:

if he shares his thoughts on how they could get their work done faster like using an app like this, then it would be of great help to them

 evaluate P(6,2) or 6p2

Answers

Answer:

30

Step-by-step explanation:

Permutation equation: [tex]\frac{n!}{(n-r)!}[/tex]

n = Total number of objects, r = Number of objects selected

[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]

Length of a line segment with endpoints (3,-2) and (-3,4).

Answers

Answer:

6squareroot2

Step-by-step explanation:

that's the answer I think

vector v has a horizontal vector component with magnitude 19 and a vertical vector component with magnitude 35. what is the acute angle theta formed by v and positive x-axis?

Answers

9514 1404 393

Answer:

  61.5°

Step-by-step explanation:

The tangent relation is useful here. The angle is opposite the vertical side and adjacent to the horizontal side of the right triangle.

  Tan = Opposite/Adjacent

  tan(α) = 35/19

  α = arctan(35/19) ≈ 61.5°

The angle made by v and the positive x-axis is 61.5°.

Let ​f(x)=−5x+18 and ​g(x)=x2+15.

Find ​f(−2​)−​g(−2​).

Answers

Answer:

21

Step-by-step explanation:

-5(-2)-(-2)²+15

10-(4)+15

10-4+15

21

Answer:

9

Step-by-step explanation:

f(x)=−5x+18

f(-2) = -5(-2)+18 = 10+18 = 28

​g(x)=x^2+15

g(-2) = (-2)^2 +15 = 4+15 = 19

f(02) - g(-2) = 28 - 19 = 9

In an experiment, the initial temperature of a solution is -5 °C. The solution is heated up at 3 °C per minute for 19 minutes and then it is cooled at 4 °C per minute for 6 minutes. Calculate the final temperature, in °C, of the solution.​

Answers

Answer:

28°C

Step-by-step explanation:

First you do 3*19=57°C

-5+57= 52°C

then you do 4*6=24 °C

as its being cooled you takeaway

52-24=28°C

if a circumference of a circle is 22cm.find it diameter take pie 22/7.

Answers

Answer:

Step-by-step explanation:

i know the answer ok it is easy

What's the distance between the points (7,3) and (7,–8)?

Answers

Answer:

11

Step-by-step explanation:

The distance is found by

d =sqrt ( (x2-x1)^2 + (y2-y1)^2)

  = sqrt( ( 7-7)^2 +(3 - -8)^2)

   = sqrt(0 +(3+8)^2)

  = sqrt( 11^2)

  = 11

 

Answer:

The distance between (7, 3) & (7, -8) is 11

Step-by-step explanation:

I used distance formula for the following explanation attached with an image.

Hope this explanation helps!

Mariah owed her grandfather 52.25 but was recently able to pay him back $1.50. How much does Mariah currently
owe her grandfather?

Answers

Subtract 1.50 from 52.25.

The answer is 50.75.

Answer:

52.25 - 1.50 = 50.75

Step-by-step explanation:

I'd recommend using a calculator or pencil and paper

53.25

-  1.50

--------

50.75

Which statement is sufficient to prove that quadrilateral ABCD is a parallelogram?


A) m∠A ≅ m∠C, m∠B ≅ m∠D

B) AB ≅ CD

C) AC ≅ BD

D) BC // AD

Answers

Answer:

A) m∠A ≅ m∠C, m∠B ≅ m∠D

Step-by-step explanation:

If both pairs of opposite angles are congruent, then the figure is a parallelogram.

How do you complete the square of x2+8x+26?

Answers

Answer:

see below

Step-by-step explanation:

x^2+8x+26

Take the coefficient of the x term

8

Divide by 2

8/2 = 4

square it

4^2 =16

we need to add 16 to 26 = 16+10

x^2 + 8x+16  +10

(x+4)^2 +10

The answer you are looking for is (x+4)²+10.

Solution/Explanation:

Selecting the "x" term's coefficient,

It would be 8.

Now, dividing it by 2,

8/2=4.

Squaring 4,

4²=16.

So, now, since (x+4)²=x²+8x+16, you must solve for 26-16, which equals 10, which you would supplement into the equation.

So, therefore, (x+4)²+10.

I hope this has helped you. Enjoy your day.

AABC is reflected across the x-axis and then translated 4 units up to create AA'BC. What are the coordinates of the vertices of AABC?

Answers

When Triangle ABC is reflected on the x-axis the new coordinates are A (-3,-1) B(-1,-3) C(-2,-1)

However the Triangle is then translated 4 units up, so the New and Final coordinates for Triangle ABC is A(-3,3) B(-1,0) and C(-2,4)

Hope this helps

HELPPPP PLZ
Witch statement is true about the value of |6|?

Answers

Answer:

The third choice is the correct one.

Step-by-step explanation:

The absolute value of six means that it's the distance from 0 to six, and that distance will be positive regardless of the number being negative or not.

Answer: The third answer is correct

Step-by-step explanation:

Since |6| is the absolute value of positive six, the value of an absolute value of any number is always positive.

the area of a rectangular park is 7/8 sqaure mile. the length of the park is 3/4 mile. what is the width of the park?

Answers

Answer:

7/6

Step-by-step explanation:

since the formula of area is length times width,you have to divide the area by the length to find the width

area=length×width

the width will be

width=area÷length

=7/8÷3/4

7/8×4/3

7/2×1/3

7/6

that's the width you can prove it by multiplying the length times the width to see if you will get 7/8..

I hope this helps

what is the aswer to 5 is 2 more than?


Answers

Answer:

Cuz 5 is greater than 2

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

What are the slope and the y-intercept of the linear function that is represented by the graph?

Answers

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
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Andrew is an avid archer. He launches an arrow that takes a parabolic path.The equation of the height of the arrow with respect to time isy = -4.9x2 + 48x, where y is the height of the arrow in meters aboveAndrew's bow and x is the time in seconds since Andrew shot the arrow.Find how long it takes the arrow to come back to a height even with his bowheight. How many of Pauls letters are undisputed?a. 5b. 7c. 9d. 11 A characteristic is a feature that helps to identify something. How would you describe a characteristic of a good movie or book? 20) solve: [tex] {8}^{2} + 2 = [/tex]21) solve: [tex]4(2x + 5y = [/tex]22) simplify the expression [tex]4( {2}^{2} + 30) - 4 = [/tex] A. Nepalese sculptures of Buddha were more realistic than Indian sculptures of Buddha B. Buddhism had spread from India to Nepal by the 11th century C. Buddhism was not practiced outside of India during the 11th century D. Buddhism had spread from Nepal to India by the 11th century why am i doing the investigation who know how to do this ? what effect does the force of gravity have on a stone thrown vertically upwards Explore the life and works of a favorite artist.Choose an artist whose work you find interesting describing the artist, his or her life, the time period, the medium in which he or she worked and one or two works You may want to peruse art books to find an artist, or you may want to choose one of the artists whose works you have seen in this lesson and look him or her up on the Internet. HELP ME PLZ FAST There is more than 1 answer,The picture is down A basketball player made 5 baskets during a game. Each basket was worth either 2 or 3 points. How many different numbers could represent the total points scored by the player? Match the answers.. Explain what it means for a solution of an equation to be extraneous. Please help right now ASAP!!!make sure your right I need help ASAP?!!!!!! Please anyone please Help me please Find the value of the variable(s). (9x + 12) 3x (4y - 10) 1 I got to my friend's house at three o'clock. They had... already played.... football for hours.(play) Select the correct answer.What is the key feature of the third-person omniscient point of view?A. It is told from the point of view of a specific character in the story.B. It is used to express the thoughts and feelings of the central character.C. It is used when directly addressing the reader or giving instructions.D. It has an all-knowing narrator who is aware of all the characters' perspectives. Is this information in the correct form for use in a letter?1608 Revere StreetBoston, MAMarch 2, 1992A.YesB.No