A college statistics class at a nearby university has 1,000 students enrolled in it. On a recent exam, the mean score was 75% with a standard deviation of 5%. Use the calculator to show what percentage of students scored between a 73 and 78 (C grade).

Answers

Answer 1

Answer:

38.11%

Step-by-step explanation:

Given that:

Mean (μ) = 75, standard deviation (σ) = 5

Z score is a measure in statistics to determine the variation of a raw score from the mean. It is given by the equation:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

To calculate the percentage of students scored between a 73 and 78 (C grade), we need to find the z score for 73 and then for 78.

For x = 73, the z score is:

[tex]z=\frac{x-\mu}{\sigma}=\frac{73-75}{5} =-0.4[/tex]

For x = 78, the z score is:

[tex]z=\frac{x-\mu}{\sigma}=\frac{78-75}{5} =0.6[/tex]

From the probability distribution table:

P(73 < x < 78) = P(-0.4 < z < 0.6) = P(z < 0.6) - P(z < -0.4) = 0.7257 - 0.3446 = 0.3811 = 38.11%


Related Questions

Stir-fry is Vince's favorite food to cook, but it always makes a lot of smoke! Vince needs to know the volume of his kitchen so he can buy a fan that is the right size. Vince's kitchen has a floor area of 85 square feet. The height of the ceiling is 8 feet. What is the volume of Vince's kitchen?

Answers

Answer:

The volume of Vince’s Kitchen is 680 cubic feet

Step-by-step explanation:

To calculate the volume of Vince’s kitchen, what is needed to be done is to multiply the area of the floor by the height of the kitchen

Mathematically Volume V of kitchen = area of kitchen floor * height of kitchen

From the question, the area of the kitchen floor = 85 square feet

Height of kitchen = 8 feet

Plugging these values to get the area of the Kitchen, we have;

V = 8 * 85 = 680 cubic feet

help plz! (a + b - c)(a + b + c) multiplying polynomials

Answers

Answer:

a^2 + 2ab + b^2 - c^2

Step-by-step explanation:

When you multiply all the terms together you get a^2 + ab + ac + ab + b^2 + bc - ac - bc - c^2. Then you can just combine like terms and simplify it to a^2 + 2ab + b^2 - c^2. Hope this helps :)

Carlos bought 80 feet of wire for ​$17.60. He needs 30 more feet. If the unit price is the​ same, how much will he pay for the extra 30 feet of wire​?

Answers

Answer:

Carlos bought 80 feet of wire for ​$17.60.

Then the price for 1 feet of wire is 17.6/80 = 0.22

=> 30 feet of wire would cost: 30 x 0.22 = 6.6

Hope this helps!

:)

Positive ÷ positive = ?

Answers

Answer:

positive

Step-by-step explanation:

The data on ages at which a sample of 35 fathers had their first child show a mean 25.43 and standard deviation 5.19. Define the population parameter of interest in this context.

Answers

Answer:

Step-by-step explanation:

A population parameter describes an entire population; a particular characteristic of an entire population. A value that describes the entire population. In this context, the population parameter is looking into the average ages of fathers when they had their first child, but this value is not given. The mean given here is the sample statistic.

Since, the population studied here is a very large population (all fathers), you have a statistic. But sometimes, if the population is very small and groups are small enough to measure, you have a parameter.

Derek is playing a prank on Grace and hid her pencil inside a tissue box that has a width of 4 inches, a length of 8 inches, and a height of 4 inches. The pencil fits perfectly from the upper left corner to the bottom right corner of the box. What is the length of Grace’s pencil to the nearest tenth of an inch?

Answers

Answer:

9.8 Inch

Step-by-step explanation:

The distance from the upper left corner to the bottom right corner of the box is the longest diagonal of the box.

For a rectangular prism:

Length of the Longest diagonal [tex]=\sqrt{ l^2+h^2+w^2}[/tex]

Therefore:

Length of the pencil[tex]=\sqrt{ 8^2+4^2+4^2}[/tex]

[tex]=\sqrt{96}\\=9.8$ inch(correct to the nearest tenth of an inch)[/tex]

Answer: length of pencil is 9.8 inches.

Step-by-step explanation:

The pencil fits perfectly from the upper left corner to the bottom right corner of the box. This is the diagonal of the box(not the diagonal of a face). To determine the length of the pencil, we would determine the length of the diagonal of the box. The formula formula is

d = √(l² + w² + h²)

Where

d = diagonal = length of pencil

w = width = 4 inches

h = height = 4 inches

l = length = 8 inches

Therefore,

d = √(4² + 4² + 8²) = √96

d = 9.8 inches

A savings account balance is compounded continuously.If the interest rate is 3.1% per year and the current balance is 1077.00 in how many years will the balance reach 1486.73?

Answers

Answer:13.8 is the best answer i could get

Step-by-step explanation:1,077 multiply that × 13.8 =14,862

Find the total volume of the rectangular prisms.
A) 88 units3
B) 96 units3
C) 104 units3
D) 114 units3

Answers

Answer:

C) 104 units^3

Step-by-step explanation:

The formula for volume in a rectangular prism is V=lwh

There are three total rectangular prisms, so take the volume of each individual prism and add them together to get the total volume.

smallest: V=(2)(2)(4) = 16

Medium: (2)(2)(6) = 24

Largest: (2)(2)(16) = 64

Add it together: 16+24+64= 104

Your answer is 104 units^3

:)

6 radians is the same as____
Round to the nearest hundredth of a degree.

Answers

Answer:

343.77

Step-by-step explanation:

1 radian is about 57.2958 degrees

so 57 times 6 is about 343.77

343.77 is your answer

when nathan was 2 1/2 years old, he was 34 inches tall. the doctor told his mother that he will be two times and 4 inches taller than that when he is an adult. which of the following equation will give h, nathans height, as an adult

Answers

Answer 5 ft 4 in

Step-by-step explanation:

2 1/2 + 2 1/2=5 + 4 inches

Sumara Kato's savings account has a balance of $1663. After 19 years, how much interest
will she have earned if her rate is 5.5% compounded annually?
(1) $3159.70 (2) $2936.27 (3) $2942.27
(4) $2925.27

Answers

Answer: $2936.27

Step-by-step explanation:

Present value = $1663

Rate = 5.5%

Time(n) = 19years

Future value= PV(1+r)^n

= 1663(1+5.5%)^19

= 1663(1.055)^19

=1663 × 2.766

=4599.86

Interest = Future value - Present value

= $4599 - $1663

= 2936

maya was asked whether the following equation is an identity (2x+3)(x+1) = 2(x+1)^2 + (x+1)

Answers

No their not the first one ends up as 2x^2 plus four x plus four the other one isn’t the same

Answer:

Maya is correct.

Step-by-step explanation:

Khan Academy gave me the answer.

can someone please help me ill give a brainliest

Answers

Answer:

C

Step-by-step explanation:

-

Answer:

yes

Step-by-step explanation:

2. 2x - y = 6,
- x + y = -1

Answers

Answer:

x = 5

y = 4

Step-by-step explanation:

just substitute the value of one variable into the other

-x +y = -1

or y = -1 +x   <-------- (i just added x to the right side)

now u know what y is equal to, just substitute that value into the first equation

2x - (-1+x) = 6     <-------- instead of y, i put the value of y from the 2 equation

NOW SOLVE FOR X!

2x +1 -x = 6

x + 1 = 6

x = 5

now solve for y since you have the value of x

y = -1 + x

or y = -1 + 5

y = 4

Answer:

y=3.166     x=4.166

Step-by-step explanation:

The total time T (in hours) needed to fly from New York to Los Angeles and back can be
modeled by the equation below, where d is the distance (in miles) each way, a is the average
speed (in miles per hour), and j is the average speed (in miles per hour) of the jet stream.
Simplify the equation. Then find the total time to the nearest minute it takes to fly 2468 miles
when a = 512 miles per hour and j = 103 miles per hour.

Answers

Answer:

complicated process just think and do the math If I was helpful pls be thnked

Step-by-step explanation:

Which statement is true about a line that contains the point ሺ2, 7ሻ and has a slope of 0.5?

A The line will also contain the point ሺ4, 6ሻ.
B The line will have a y-intercept of 6.
C The line will contain points whose y-coordinate will decrease in value as you move to the right
D none of the above

Answers

Answer:

I think it is C) The line will contain points whose y-coordinate will decrease in value as you move to the right

Step-by-step explanation:

HOPE THIS HELPS

Mr. Stewart used a gallon of vinegar to make 15 different color egg dipping containers. He used the same amount of vinegar in each container. How much vinegar in gallons was used in each egg dye container?

Answers

Answer:

0.067 gallons ( to 2 decimal places)

Step-by-step explanation:

First, note that since the same amount of vinegar was used in each container, it means that the 1 gallon of vinegar was divided equally to the 15 containers, hence the amount of vinegar used in each dye container is calculated as follows:

total volume of vinegar = 1

number of egg dye containers = 15

if equal volume of vinegar was used in each container:

volume of vinegar in each egg dye container = 1 ÷ 15 = 0.067 gallons ( to 2 decimal places)

j divided by 9 is 5 , write an equation to represent the following statement

Answers

Answer:

The first answer is incorrect

Step-by-step explanation:

45 divided by 9 is 5 not 40

The equation that represents the statement is j / 9 = 5.

What is an Equation?

An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.

The statement j divided by 9 is 5 can be written in equation form as follows:

j / 9 = 5

j = 45

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A mirror should be centered on a wall the mirror is 4 feet wide in the wall is 20 Feet wide what equation helps determine the distance X on each side of the mirror

Answers

Answer:

A)x + 4 + x = 20

Step-by-step explanation:

Complete question:

Which equation helps determine the distance x on each side of the mirror?

A. x + 4 + x = 20

B. 4 + x + 4 = 20

C. x = 20 + 4 + 4

D. 4 = 20 + x + x

SOLUTION:

As given,The mirror is 4 feet wide and the wall is 20 feet wide.

The distance 'x' on each side of the mirror is x + x

4 feet wide + x + x = 20 feet wide

The mirror 4 feet wide + the distance x on each side of the mirror = the wall is 20 feet wide

Therefore, the correct option is A

If you are given a paper which has lines which are the length of a needle apart, and then you repeated drop that needle onto the paper, the probability that the needle with cut the line is:

Answers

Answer:

The correct option is;

[tex]\frac{1}{\pi }[/tex]

Step-by-step explanation:

Here we have that

[tex]Probability = \frac{Number \, of \, required\, outcomes}{Number \, of \, possible\ outcomes} = \frac{Dimension \, of \, the \, line}{Size \, of \, the \ needle} = \frac{l \times D}{\pi \times D \times l } = \frac{1}{\pi }[/tex]

Therefore, the probability that the needle will cut the line = 1/π.

What is the area of the triangle (I need this today pls help)

Answers

Answer: 24 units^2

(12*4)/(2)=24

Step-by-step explanation:

Answer:

Step-by-step explanation:

4*12/0.5=96

The diagram shows a square-based cuboid.
10 cm
4 cm
Work out the volume of the cuboid.
State the units of your answer.

Answers

Answer:

400 cubic cm

Step-by-step explanation:

Given that base is square and is side is 10 cm

area of square is given by side^2

Thus, area of base of cuboid  = [tex]10^2[/tex] square cm = 100 sq. cm

We know volume for any cuboid is area of base * height

height is 4cm

thus, volume of cuboid = area of base of cuboid * height

                                     = 100 * 4 cubic cm = 400 cubic cm

Volume of cuboid is 400 cubic cm.

Unit is cubic cm

The volume of square based cuboid is [tex]400cm^{3}[/tex].

Given that, base is square and side of base is 10 cm.

Height of the square-based cuboid.is 4cm.

Area of base = [tex](side)^{2}=(10)^{2}=100cm^{2}[/tex]

Volume of the cuboid is multiplication of base area and height of the cuboid.

  [tex]Volume=100*4=400cm^{3}[/tex]

Hence, the volume of square based cuboid is [tex]400cm^{3}[/tex].

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Hunter earned a grade of 5% on his multiple-choice math final that had a total of 60 problems. How many problems on the final exam did Hunter answer correctly?

Answers

Answer:

3

Step-by-step explanation:

From the information given in the statement, you can find the number of problems that Hunter answered correctly by calculating the 5% of 60. This because 5% is the grade that he got which means that he only had 5% of his answers correctly and 60 is the total number of problems:

60*5%= 3

According to this, Hunter answered correctly 3 problems on the final exam.

Solve 8.2ws 29.52. Which of the following must be true abo
OWS36
The arrow points left
The arrow points right
There is an open circle at 3.6.
There is a closed circle at 3.6.

Answers

Answer:

A B E

Step-by-step explanation:

A- w less-than-or-equal-to 3.6

B- The arrow points left.

E- There is a closed circle at 3.6.

Answer:

A B E

Step-by-step explanation:

Solve the system of inequalities and indicate all the integers which are in the solution set:
[tex]\left \{ {{3-2a\ \textless \ 13} \atop {5a\ \textless \ 17}} \right.[/tex]

Answers

Answer:

-5 < a < 3.4

Step-by-step explanation:

3 - 2a < 13

3 - 13 < 2a

2a > -10

a > -5

5a < 17

a < 3.4

Solution:

-5 < a < 3.4

Step-by-step explanation:

Step 1:  Find the solution to the first equation

[tex]3 - 2a < 13[/tex]

[tex]3 - 3 - 2a < 13 - 3[/tex]

[tex]-2a < 10[/tex]

[tex]-2a / -2 < 10 / -2[/tex]

[tex]a > -5[/tex]

Step 2:  Find the solution to the second equation

[tex]5a < 17[/tex]

[tex]5a / 5 < 17 / 5[/tex]

[tex]a < 3.4[/tex]

Answer:  [tex]-5 < a < 3.4[/tex]

What is the error in the flow chart

Answers

there is no flow chart

Answer:

WHAT FLOWCHART?

Step-by-step explanation:

find angle C! please and thankyou

Answers

Answer: it's around 40

Step-by-step explanation:

Which represents the solution(s) of the system of equations, y = -x2 + 6x + 16 and y = - 4x + 37? Determine the solution set
algebraically
O (325)
(-3, 49)
(3,25) and (79)
(-3, 49) and (-7, 65)

Answers

Answer:

The answer is c

Step-by-step explanation:

(7,9) (3,25)

The solution sets of the given system of equations are (3,25) and (7,9).

Given equations are :

[tex]y=-x^{2} +6x+16[/tex]........(1)

[tex]y=-4x+37[/tex]...........(2)

What is an equation?

An equation is a statement that equates to two expressions.

So, for the solutions of the  given system of equations

[tex]-x^{2} +6x+16=-4x+37[/tex]

[tex]x^{2} -10x+21=0[/tex]

[tex]x^{2} -3x-7x+21=0\\x(x-3)-7(x-3)=0[/tex]

[tex](x-3)(x-7)=0[/tex]

So, [tex]x=3[/tex]

[tex]x=7[/tex]

Corresponding y value for x=3

[tex]y=-4*3+37\\y=25[/tex]

Corresponding y value for x=7

[tex]y=-4*7+37[/tex]

[tex]y=9[/tex]

Hence, the solution sets of the given system of equations are (3,25) and (7,9).

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Find the slope of the line passing through the poin (- 3, 7) (2, - 6)

Answers

Answer:

[tex] \frac{13}{ - 5} [/tex]

Step-by-step explanation:

[tex] \frac{y1 - y2}{x1 - x2} \\ \frac{7 - ( - 6)}{ - 3 - 2} \\ \frac{7 + 6}{ - 5} \\ = \frac{13}{ - 5} [/tex]

Answer:

-2.6

Step-by-step explanation:

Slope or gradient is the ratio of the vertical (y axis) and horizontal distances (x axis) between two points on a line.

It should be noted that it is defined as zero if the line is horizontal, but undefined if it is vertical.

Given:

Coordinates (- 3, 7) (2, - 6)

y1 = 7, y2= -6, x1= -3, x2=2

Slope : ∆ y/ ∆ x

= (y2 - y1 )/ (x2 - x1)

= (-6 - (7))/ (2 - (-3))

= (-13)/(5) = -13:5= -2.6

Factor the expression 2x4y – 18x2y3 completely.

A. 2x2y(x2 – 9y2)

B. 2x2y(x – 3y)(x + 3y)

C. 2x2y(x – 3y)2

D. 2x2y(x – 9y)(x + 2y)

Answers

Answer:

B

Step-by-step explanation:

[tex]2x^{4}y - 18x^{2}y^{3}[/tex]

Both sides have [tex]x^{2}[/tex]

[tex]x^{2} (2x^{2}y - 18y^{3})[/tex]

Both sides have y

[tex]yx^{2} (2x^{2} - 18y^{2})[/tex]

Both sides have 2

[tex]2yx^{2} (x^{2} - 9y^{2})[/tex]

Rule : [tex]x^{2} - y^{2} = (x+y)(x -y)[/tex]

[tex]x^{2} = x.x\\9y^{2} = 3y. 3y[/tex]

[tex](x^{2} - 9y^{2}) = (x +3y) (x-3y)[/tex]

Final:

[tex]\red{ 2 {x}^{2} y(x - 3y)(x + 3y)}[/tex]

Hope this helps ^-^

The factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.

What is Factorization?

The act of expressing a number or other mathematical object as the sum of numerous factors is known as factorization.

The given expression is 2x⁴y-18x²y³.

Factor the expression as follows:

2x⁴y-18x²y³

= 2x²y(x² - 9y²)

= 2x²y(x² - (3y)²)

= 2x²y(x + 3y)(x- 3y)

Hence, the factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.

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