Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was 533 with a margin of error of 27 . Which of the following is a reasonable value for the true mean SAT score of graduating high school seniors?
565.7
516
493.9
564.6

A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was $533$ with a margin of error of $27$ . Which of the following is a reasonable value for the true mean SAT score of graduating high school seniors? $\newline$ $565$ . $7$ $\newline$ $516$ $\newline$ $493$ . $9$ $\newline$ $564$ . $6$

View step-by-step help

View step-by-step help

Scale drawings: word problems

Full solution

Q. A study by the department of education of a certain state was trying to determine the mean SAT scores of the graduating high school seniors. The study found that the mean SAT score was

533

with a margin of error of

27

. Which of the following is a reasonable value for the true mean SAT score of graduating high school seniors?

\newline

565

.

7

\newline

516

\newline

493

.

9

\newline

564

.

6

Understand Margin of Error: Understand the concept of margin of error. The margin of error in a statistical study is the range within which we can expect the true mean to lie with a certain level of confidence. In this case, the margin of error is $27$ points.
Calculate Lower Bound: Calculate the lower bound of the mean SAT score. Subtract the margin of error from the given mean to find the lowest possible value of the true mean. Lower bound = Mean SAT score - Margin of error = $533 - 27 = 506$
Calculate Upper Bound: Calculate the upper bound of the mean SAT score. Add the margin of error to the given mean to find the highest possible value of the true mean. Upper bound = Mean SAT score + Margin of error = $533 + 27 = 560$
Determine Valid Values: Determine which of the given values fall within the calculated range. $\newline$ We have established that the true mean SAT score should be between $506$ and $560$ . Now we need to check which of the given values fall within this range. $\newline$ - $565.7$ is greater than $560$ , so it is not a reasonable value. $\newline$ - $516$ is between $506$ and $560$ , so it is a reasonable value. $\newline$ - $493.9$ is less than $506$ , so it is not a reasonable value. $\newline$ - $564.6$ is greater than $560$ , so it is not a reasonable value.

More problems from Scale drawings: word problems

Question

A factory designs cylindrical cans

10 \mathrm{~cm}

in height to hold exactly

500 \mathrm{~cm}^{3}

of liquid. Which of the following best approximates the radius of these cans?

\newline

1

\newline

4 \mathrm{~cm}

\newline

8 \mathrm{~cm}

\newline

12.5 \mathrm{~cm}

\newline

15.9 \mathrm{~cm}

Posted 7 months ago

Question

A die is created by smoothing the corners of a plastic cube and carving indented pips. The original cube had an edge length of

2

(\mathrm{cm})

. The volume of the final die is

7.5 \mathrm{~cm}^{3}

. What is the volume of the waste generated by creating the die from the cube in

\mathrm{cm}^{3}

Posted 4 months ago

Question

We want to find the intersection points of the graphs given by the following system of equations:

\newline

\left\{\begin{array}{l} y=2 x-1 \\ x^{2}+y^{2}=1 \end{array}\right.

\newline

One of the intersection points is

(0,-1)

\newline

Find the other intersection point. Your answer must be exact.

Posted 8 months ago

Question

A(x)=(8+2 x)^{2}

\newline

Carmen wants to add a border around a square picture. The function shows the area of the picture in square inches if it has a border

x

inches wide. What are the dimensions of the picture without the border?

\newline

1

\newline

2

2

\newline

6

6

\newline

8

8

\newline

10

10

Posted 10 months ago

Question

s=-11.8(t-1.2)^{2}+17

\newline

The equation models the horizontal distance,

s

, in centimeters, of a particular image on a computer screen from the left-hand edge of the screen,

t

seconds after appearing. If the image moves in from the left-hand edge of the screen during an on-screen animation, how far to the right does the image travel?

\newline

1

\newline

1

2

\newline

5

2

\newline

17

\newline

34

Posted 10 months ago

Question

A soap company changes the design of its soap from a cone to a sphere. The cone had a height of

3

(\mathrm{cm})

and a radius of

2 \mathrm{~cm}

. The sphere has a diameter of

3 \mathrm{~cm}

. The new design contains

\frac{\pi}{f}

cubic centimeters more soap than the old design. What is the value of

f

Posted 7 months ago

Question

Mindy is a sculptor. She has a cylinder of stone with a radius of

3

(\mathrm{m})

and a height of

2 \mathrm{~m}

. She needs to carve out a sphere of radius

1 \mathrm{~m}

from the cylinder. Mindy must cut away

\frac{v}{3} \pi

\left(\mathrm{m}^{3}\right)

of stone from the cylinder in order to be left with the sphere. What is the value of

v

Posted 3 months ago

Question

A cylindrical soda can has a volume of

108 \pi

cubic centimeters

\left(\mathrm{cm}^{3}\right)

and a height of

12 \mathrm{~cm}

. What is the surface area of the soda can in square centimeters?

\newline

1

\newline

18 \pi \mathrm{cm}^{2}

\newline

36 \pi \mathrm{cm}^{2}

\newline

72 \pi \mathrm{cm}^{2}

\newline

90 \pi \mathrm{cm}^{2}

Posted 8 months ago

Question

\mathrm{Cleo}

are looking for a location to open their new yoga studio. A fellow studio owner suggests a location that will fit

28

756

square foot area. Assuming that each student has a spot

x

3

times as long, what is the length, in feet, of the space they are allotting to each student?

\newline

1

\newline

1

\newline

3

\newline

9

\newline

27

Posted 7 months ago

Question

Morgan is designing a rectangular quilt. The quilt will be

1 \frac{3}{5} \mathrm{~m}

wide and will have an area of

6 \mathrm{~m}^{2}

\newline

How long is the quilt?

\newline

Posted 8 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant