A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1070 and a standard deviation of 204. Scores on the ACT test are normally distributed with a mean of 19.1 and a standard deviation of 5.2. It is assumed that the two tests measure the same aptitude, but use different scales.
(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score. Round answer to a whole number. SAT score =
(B) What would be the equivalent ACT score for this student? Round answer to 1 decimal place. ACT score =
(C) If a student gets an SAT score of 1417, find the equivalent ACT score. Round answer to 1 decimal place. ACT score =

Answers

Answer 1

Answer:

a) SAT score = 1075

b) ACT score = 19.2.

c) ACT score = 27.9.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

(A) If a student gets an SAT score that is the 51-percentile, find the actual SAT score

SAT scores have mean 1070 and standard deviation 204, so [tex]\mu = 1070, \sigma = 204[/tex]

51th percentile means that Z has a p-value of 0.51, so Z = 0.025. The score is X. So

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

[tex]0.025 = \frac{X - 1070}{204}[/tex]

[tex]X - 1070 = 0.025*204[/tex]

[tex]X = 1075[/tex]

SAT score = 1075.

(B) What would be the equivalent ACT score for this student?

ACT scores have mean of 19.1 and standard deviation of 5.2, which means that [tex]\mu = 19.1, \sigma = 5.2[/tex]. The equivalent score is X when Z = 0.025. So

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

[tex]0.025 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 0.025*5.2[/tex]

[tex]X = 19.2[/tex]

ACT score = 19.2.

(C) If a student gets an SAT score of 1417, find the equivalent ACT score.

Z-score for the SAT:

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

[tex]Z = \frac{1417 - 1070}{204}[/tex]

[tex]Z = 1.7[/tex]

Equivalent score on the ACT:

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

[tex]1.7 = \frac{X - 19.1}{5.2}[/tex]

[tex]X - 19.1 = 1.7*5.2[/tex]

[tex]X = 27.9[/tex]

ACT score = 27.9.


Related Questions

What number must you add to the polynomial below to complete the square?

x2 + 15x

Answers

Answer:

The number [tex]\frac{225}{4}[/tex] is added to the polynomial below to complete the square.

Step-by-step explanation:

Perfect square binomial:

A perfect square binomial is given by:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

In this question:

We have that:

[tex]a^2 + 2ab + b^2 = x^2 + 15x + ?[/tex]

Since [tex]a = x[/tex], we have that:

[tex]2ab = 15x[/tex]

[tex]2b = 15[/tex]

[tex]b = \frac{15}{2}[/tex]

Completing the square:

The term that completes the square is [tex]b^2[/tex]. So

[tex]b^2 = (\frac{15}{2})^2 = \frac{225}{4}[/tex]

The number [tex]\frac{225}{4}[/tex] is added to the polynomial below to complete the square.

Use the shapes to answer the questions that follow:

Answers

Answer:

50%

Step-by-step explanation:

Theres 10 shapes and 5 of them are yellow. So that is 5/10 which equals 50%

hope this helps <3

Answer:

50%

Step-by-step explanation:

5/10 are yellow so 5% I think

5.
Multiply.
(3x + 2)(x - 3)

Answers

Answer: 3x^2 - 7x - 6

Step-by-step explanation:

Answer:

3x^2-7x-6

Step-by-step explanation:

(3x+2)(x-3)

3x^2-9x+2x-6

3x^2-7x-6

Hope this helps.

Simplify to a single power of 2

Answers

128? I think because 2x2 than 2x2x2x2x2 is 32 than 32x4

Answer:

2^7

Explanation:

You can add up the square of two and the square of five. This is the easiest way.

Simplify the following expression.

1/2 divided by 1/10

A. 1 whole 1/3




B. 1/20



C. 5


D. 1/5

Answers

Answer:

I got C.)5

Step-by-step explanation:

Candice and Joe went to Sawcon, the concert tickets for the concert Sawcon was 50 dollars each person. Plus tax they add 2.5 dollars. Since they have a discount they minus 10.5. How much are the tickets now?

Answers

Answer:

they would be $42.00

Step-by-step explanation:

50 + 2.50= 52.50

52.50-10.50=42.00

Find the measure of angle 3

Answers

Answer:

120

Step-by-step explanation:

What will be the coordinates of the image after a translation up 4 units and right 6 units

Answers

Answer:

B

Step-by-step explanation:

To find the answer, translate each point and then use the process of elimination.

For the first point, the coordinates are (-4, -2). The -4 is x and the -2 is y. Translations up and down relate to the y value, while translations left and right relate to x. To translate up 4 units, add 4 to the y value of the coordinate. -2 + 4 is 2, so the y coordinate of the first point will be 2. That eliminated A and D.

For the second point, translate up 4 units (-5 + 4) and you get -1. So the y value of the second point will be -1. In option C, it is positive 1. So that leaves only B.

5th grade math. correct answer will be marked brainliest

Answers

Answer:

5280

Step-by-step explanation:

Hope this helps!

Can anyone please help me with this? i need answers for all the blank spaces. I dont need to know how to do it, just the answers.

Answers

Answer:

[tex]\\(x- -1)^{2} + (y- -1)^{2} = 13[/tex]

so, -1, -1 and 13

Please help me. Image below.

Answers

Answer:

10 cubes

Step-by-step explanation:

2.5 × 1 × 2 = 5 cm³

5 ÷ 0.5

10 cubes

Answer:

10 cubes

Step-by-step explanation:

1 × 2 × 2.5 = 5cm^3

5 ×× .5 = 10

so 10 cubes would fit

PLEASE HELP
On the graph below, Point A is located at the intersection of angle θ and the unit circle.
What are the exact coordinates of point A?

Use the on-screen keyboard to type the answer in the box below.

https://imgur.com/a/UwbnsCV

Answers

Answer:

  1/2,

Step-by-step explanation: Please find the attached image of unit circle.

We have been given that the measure of angle t is 60 degrees. We are asked to find the x-coordinate of the point where the terminal side intersects the unit circle.

We know that x-coordinate on unit circle represents cosine and y-coordinate represents sine of a given angle.

We can see from our attachment that x-coordinate of the point at angle 60 degrees is , therefore, x-coordinate of the angle of 60 degrees, where the terminal side intersects the unit circle is .  

expand : log3(x^3/81y^2)

Answers

Answer:

Use rules of logarithms to expand.

2

log

3

(

x

)

4

4

log

3

(

y

)

Step-by-step explanation:

Plsss help I am falling

Answers

Answer:

that sucks

Step-by-step explanation:

srry man i got nothin

Find the area of the shaded figure in the diagram below. Use 3.14 for π and round your answer to the nearest hundredth.

A. 39.57in^2
B. 66.89 in^2
C. 200.67 in^2
D. 118.72 in^2

Answers

Answer:

D

Step-by-step explanation:

diameter of 1 circle = 21.3/3= 7.1

radius of 1 circle= 7.1/3=3.55

area of 1 circle =πr^2=3.14× (3.55)^2=39.57

area of 3 circle= 39.57×3=118.72

therefore,area of shaded portion= area of 3 circle =118.72

Need help on the picture i attached

Answers

Answer:

1.) Standard form -            

2.) Center (1,-3)

3.) Radius r=4

4.) Diameter d=8

5.) Circumference 25.12

6.) Area 50.24

7.) Graph              

Step-by-step explanation:

If a1 = 6 and an
-5an-1 + 4 then find the value of a4.


Help

Answers

Answer:

A4

Step-by-step explanation:

In London today, twice the low temperature was less than three times
the low temperature minus ten. In interval form, what are the possible
temperatures?

Answers

I need more information

Find the missing side of each right triangle (Pythagorean’s #Theorem)

Answers

Answer:

3

Step-by-step explanation:

The formula for the Pythagorean's Theorem is a^2 + b^2 = c^2, so first you know that hypotenuse is the longest side or the opposite side from which the right angle is which in this case is the 6 so you are looking for a leg rather then the hypotenuse which means we are going to be doing subtraction.

a^2 + b^2 = c^2

√27^2 - b^2 = 6^2

27 - b^2 = 36

-27            -27

         b^2 = 9

         b^2 = √9

         b = 3

Does anyone know the answer

Answers

Answer:

d = 126, z = 28

Step-by-step explanation:

The angle with the variable is diagonal from the 105 degree angle. In this case, that means that they are equivalent. So, 105+21 = 126. d = 126 :)

25) Margie needs to borrow $9,000 from a local bank. The
loan has a 8.5% interest rate for 4 years. What will
Margie's monthly payment be?
A) $ 221,850.00
B) $3060.00
C) $250.0
D) $ 221.85

Answers

Answer:

B) $3060.00

Step-by-step explanation:

8.5% of 9,000 equals 765, then 765 multiplied by 4 equals 3060.

I think that it will take Margie 4 years to pay back the bank. And the interest rate that the bank charges is 8.5% per month.

I'm not sure if this is correct

find the rule for the following geometric sequence: 4, -12, 36, -108, ....what is n7

Answers

Answer:

the rule is *-3,n7=-2916

Step-by-step explanation:

n4=108

n5=108*-3=-324

n6=-324*-3=972

n7=972*-3=-2916

The Unit Circle

Determine the coordinates of the point on the unit circle corresponding to the given central angle. If necessary, round your results to the nearest hundredth.
29°

a. (0.87, 0)
b. (0.87, 0.48)
c. (0.48, 0.87)
d. (1, 0.48)

Please select the best answer from the choices provided

Answers

Answer:

B. (0.87, 0.48)

Step-by-step explanation:

I calculated it logically

PLSSS HELP PANICKING
The sum of Alex and John's money is $48. Alex has $3 more than twice the amount John has. How much money do they each have? ​

Answers

Answer:

John has $15 and Alex has $33

Step-by-step explanation:

a systems of equations can be made from the information on the problem

x+y=48

x=2y+3

since x= 2y+3 substitute 2y+3 in the firat equation to get:

(2y+3)+y=48  -> 3y+3=48 -> 3y=45  -> y=15

plug in 15 for y in the second equation to solve for x

x+15 =48 --> x=33

Which statement is true?

Group of answer choices

An equilateral triangle is never an acute triangle.

An isosceles triangle is sometimes a scalene triangle.

An acute triangle is always an equilateral triangle.

A equilateral triangle is always an isosceles triangle.

Answers

Answer:

An equilateral is always an isosceles triangle.

Step-by-step explanation:

Kdksksksnsksksnssnzhzhs

Solve the following quadratic function by utilizing the square root method. f(x) = 1 - x2 x = + [?]

Answers

Answer: 1

Step-by-step explanation:

If x = 0

then, f(x) = 1 - 0

f(x) = 1

x = ±1

Let f(x)=0

1-x²=0-x²=-1x²=1x=±1

Hello Good morning can someone give me the answer of this operation?

39 + 1 - 24 / 6=

Also can you tell me the order? :> Thanks!!

Answers

Answer:

The answer is 36

Step-by-step explanation:

Because 39+1=40

So then 40-24=16

and then divided by 6 is 36 because when you divide you multiply

PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

1 and 2 is The first one and 3 and 5 is the second one

If f(1)=1, f(2)=4 and f(n)=3f(n-1)-f(n-2) then find the value of f(4).

Answers

Answer:

29

Step-by-step explanation:

f(3)=3f(2)-f(1)=3x4-1=11

f(4)=3f(3)-f(2)=3x11-4=29

Plsss help. giving extra points if correct.

Answers

Answer:

B. ACB AND ACD

Step-by-step explanation:

since you need to prove, you need to show that the figure can work on any 2 triangles… hope it helps.

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