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

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

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 .  

PLEASE HELP ILL GIVE BRAINLIEST

Answers

Answer:

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

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


Help

Answers

Answer:

A4

Step-by-step explanation:

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.

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

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

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.

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

5th grade math. correct answer will be marked brainliest

Answers

Answer:

5280

Step-by-step explanation:

Hope this helps!

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

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:

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.

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:

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

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:

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

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

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

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.

Plsss help I am falling

Answers

Answer:

that sucks

Step-by-step explanation:

srry man i got nothin

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

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

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 :)

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

Find the measure of angle 3

Answers

Answer:

120

Step-by-step explanation:

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

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

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.

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