Scores on the SAT are approximately normally distributed. One year, the average score on the Math SAT was 500 and the standard deviation was 120. What was the score of a person who did better than 85% of all the test-takers

Answers

Answer 1

Answer:

The score of a person who did better than 85% of all the test-takers was of 624.44.

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.

One year, the average score on the Math SAT was 500 and the standard deviation was 120.

This means that [tex]\mu = 500, \sigma = 120[/tex]

What was the score of a person who did better than 85% of all the test-takers?

The 85th percentile, which is X when Z has a p-value of 0.85, so X when Z = 1.037.

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

[tex]1.037 = \frac{X - 500}{120}[/tex]

[tex]X - 500 = 1.037*120[/tex]

[tex]X = 624.44[/tex]

The score of a person who did better than 85% of all the test-takers was of 624.44.


Related Questions

An isosceles right triangle has a hypotenuse that measures 4√2 cm. What is the area of the triangle?

PLEASE HELP

Answers

Answer:

8

Step-by-step explanation:

As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8

Which function below has the following domain and range?
Domain: {-7, - 5,2, 6, 7}
Range: {0, 1,8}

Answers

Answer:

{(2,0),(-5,1),(7,8),(6,0),(-7,1)

Simplificar expresiones algebraicas

Answers

Use Socratic it helps

Lakisha wants to buy some bitcoins. The exchange rate is $1 USD to 0.004 bitcoin. How many bitcoins can she buy with $400?

Answers

Answer:

1.6 Bitcoins

Step-by-step explanation:

Given data

We have the rate as

$1 USD to 0.004

Hence $400 will buy x bitcoins

Cross multiply to find the value of x

1*x= 400*0.004

x=1.6

Hence $400 will get you 1.6 Bitcoins

Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%

Answers

Answer:

x = 50

y = 50

Step-by-step explanation:

[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]

.12(100-y) + .38y = 25

x = 50

y = 50

what is the measure of m?

Answers

(6+18)^2 = m^2 + m^2
=> 2m^2 = (24)^2
=> m = 24/sqrt(2)

The required value of m for the given triangle is given as m = 12.

What are Pythagorean triplets?  

In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.

Here,
Applying Pythagoras' theorem,
n² = m² - 6² - - - - (1)

m ² + base² = 24²
base² = 24² - m² - - - - (2)

n² + 18² = base²
From equation 1 and 2
m² - 6² + 18² = 24² - m²
2m² = 24² + 6² - 18²
m = 12

Thus, the required value of m for the given triangle is given as m = 12.

Learn more about Pythagorean triplets here:

brainly.com/question/22160915

#SPJ2

Can someone help please

Answers

9514 1404 393

Answer:

  (b)  f(x) = (-x)^(1/2)

Step-by-step explanation:

The square root is only defined for argument values that are non-negative. Hence the domain of ...

  f(x) = (-x)^(1/2)

is all values of x less than or equal to zero. This is not "all values of x."

Round each of the following numbers to four significant figures and express the result in standard exponential notation: (a) 102.53070, (b) 656.980, (c) 0.008543210, (d) 0.000257870, (e) -0.0357202

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Rounding each number to 4 significant figures and expressing in standard notation :

(a) 102.53070,

Since the number starts with a non-zero, the 4 digits are counted from the left ;

102.53070 = 102.5 (4 significant figures) = 1.025 * 10^2

(b) 656.980,

Since the number starts with a non-zero, the 4 digits are counted from the left ; the value after the 4th significant value is greater than 5, it is rounded to 1 and added to the significant figure.

656.980 = 657.0 (4 significant figures) = 6.57 * 10^2

(c) 0.008543210,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.008543210 = 0.008543 (4 significant figures) = 8.543 * 10^-3

(d) 0.000257870,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

0.000257870 = 0.0002579 (4 significant figures) = 2.579 * 10^-4

(e) -0.0357202,

Since number starts at 0 ; the first significant figure is the first non - zero digit ;

-0.0357202 = - 0.03572 (4 significant figures) = - 3.572* 10^-2

Question 4 of 10
If A = (-1,-3) and B = (11,-8), what is the length of AB?
A. 12 units
B. 11 units
C. 14 units
D. 13 units
SUBMIT

Answers

Step-by-step explanation:

AB = square root of [(xA-xB)^2+(yA-yB)^2]

AB=Squarerootof(-1-11)^2 +(-3-(-8))^2=Squarerootof(-12)^2+(5)^2)

AB=Squarerootof((144)+25)= Squarerootof(169)=13 the answer is 13 units

The choice D is the right one

The cost of producing a custom-made clock includes an initial set-up fee of $1,200 plus an additional $20 per unit made. Each clock sells for $60. Find the number of clocks that must be produced and sold for the costs to equal the revenue generated. (Enter a numerical value.)

Answers

Answer:

30 clocks

Step-by-step explanation:

Set up an equation:

Variable x = number of clocks

1200 + 20x = 60x

Isolate variable x:

1200 = 60x - 20x

1200 = 40x

Divide both sides by 40:

30 = x

Check your work:

1200 + 20(30) = 60(30)

1200 + 600 = 1800

1800 = 1800

Correct!

a triangle has sides of 6 m 8 m and 11 m is it a right-angled triangle?​

Answers

Answer:

No

Step-by-step explanation:

If we use the Pythagorean theorem, we can find if it is a right triangle. To do that, set up an equation.

[tex]6^{2}+8^{2}=c^2[/tex]

If the triangle is a right triangle, c would equal 11

Solve.

[tex]36+64=100[/tex]

Then find the square root of 100.

The square root of 100 is 10, not 11.

So this is not a right triangle.

I hope this helps!

What is the length of Line segment A C? Round to the nearest tenth.

Triangle A B C is shown. Angle A C B is 90 degrees and angle B A C is 55 degrees. The length of C B is 15 meters.

10.5 m
12.3 m
18.3 m
21.4 m

Answers

Answer:

10.5

Step-by-step explanation:

In the picture if you think about it, it has to be a number less than 15 since CB is 15. I picked 12.3 and got it wrong therefore it has to be 10.5.

Answer:

A) 10.5

Step-by-step explanation:

Lost-time accidents occur in a company at a mean rate of 0.8 per day. What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2

Answers

Answer:

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Step-by-step explanation:

We have the mean during the interval, which means that the Poisson distribution is used.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

Lost-time accidents occur in a company at a mean rate of 0.8 per day.

This means that [tex]\mu = 0.8n[/tex], in which n is the number of days.

10 days:

This means that [tex]n = 10, \mu = 0.8(10) = 8[/tex]

What is the probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2?

This is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-8}*8^{0}}{(0)!} = 0.00034[/tex]

[tex]P(X = 1) = \frac{e^{-8}*8^{1}}{(1)!} = 0.00268[/tex]

[tex]P(X = 2) = \frac{e^{-8}*8^{2}}{(2)!} = 0.01073[/tex]

So

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.00034 + 0.00268 + 0.01073 = 0.01375[/tex]

0.01375 = 1.375% probability that the number of lost-time accidents occurring over a period of 10 days will be no more than 2.

Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).

Answers

Answer:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

Step-by-step explanation:

Hi there!

Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope

1) Determine the slope

[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (-2, 6) and (3,-2):

[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]

Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

2) Plug in a point [tex](x_1,y_1)[/tex]

[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]

We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:

[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]

OR

[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]

I hope this helps!

Find the intersection of the line and the circle given below
2x+y=-5
x^2+y^2=10

Answers

Answer:

There are two intersections.

(-3,1) and (-1,-3)

Step-by-step explanation:

Answer:

They intersect at (-3,1), and also (-1,-3)

Step-by-step explanation:

Graph:

(4-1) + (6 + 5) = help plz

Answers

The right answer is D!

A rope is 56 in length and must be cut into two pieces. If one piece must be six times as long as the other, find the length of each piece. Round your answers to the nearest inch, if necessary.

Answers

Answer:

48, 6

Step-by-step explanation:

The ratio of the pieces is 6 to 1

Add them together to get the total

6+1 = 7

Divide the total length by 7

56/7 = 8

Multiply the ratios by 8

6*8 = 48

 1*8 = 6

The peices are 48 and 6

Determine the domain and range of the graph

Answers

Answer:

5 ≤ x ≤ 10             5 ≤ y ≥ -1

Step-by-step explanation:

I’m in summer school can y’all plz help me

Answers

Answer:  Choice A.   [tex]-x^2+2x+8[/tex]

Work Shown:

[tex](f - g)(x) = f(x) - g(x)\\\\(f - g)(x) = (2x+1) - (x^2-7)\\\\(f - g)(x) = 2x+1 - x^2+7\\\\(f - g)(x) = -x^2+2x+(1+7)\\\\(f - g)(x) = -x^2+2x+8\\\\[/tex]

which shows the answer is choice A.

Side note: be sure to distribute the negative to every term inside the second set of parenthesis. So you wouldn't say -(x^2-7) = -x^2-7. If you did this error, then you'd get to the wrong answer choice C.

Answer:

hope it helps u plz mark me brainliest mate

Step-by-step explanation:

(f-g)(x)=2x+1-(x^2-7)

(f-g)(x)=2x+1-x^2+7

(f-g)(x)= -x^2+2x+8

this is the correct answer

Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.

Answers

Answer:

4 e

Step-by-step explanation:

dz6dxrx xrrx6 xz33x4xr4x xrx

What are the equations of the asymptotes for the functiony=tan2pix where 0

Answers

9514 1404 393

Answer:

  (b)  x = 0.25, 0.75, 1.25, 1.75

Step-by-step explanation:

The asymptotes of tan(α) are found at ...

  α = π/2 +nπ

We want to find x such that ...

  2πx = α = π/2 +nπ

Dividing by 2π gives ...

  x = 1/4 +n/2 . . . . . . . for integers n

In the desired range, the values of x are ...

  x = 0.25, 0.75, 1.25, 1.75

A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?​

Answers

Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.

He wants to end up with a 44 mL solution, so

x + y = 44 mL

Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain

0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL

of acid.

Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives

0.04x + 0.15 (44 mL - x) = 5.28 mL

0.04x + 6.6 mL - 0.15x = 5.28 mL

1.32 mL = 0.19x

x ≈ 6.95 mL

==>   y ≈ 37.05 mL

Please look at the file below. (No links will give brainiest)

Answers

Answer:

3.564 m^2

Step-by-step explanation:

The area of the original garden is

A = 5.4 * 1.5 = 8.1

The new garden is

5.4*1.2 = 6.48 by 1.5*1.2 =1.8

The area is

A = 6.48*1.8=11.664

The increase in area is

11.664-8.1=3.564

The given information is,

To find the increase in area of the garden.

Formula we use,

→ Area = Length × Width

Area of the real garden is,

→ 5.4 × 1.5

→ 8.1 m

The new garden will be,

→ 5.4 × 1.2 = 6.48 m

→ 1.5 × 1.2 = 1.8 m

The area of the new garden is,

→ 6.48 × 1.8

→ 11.664

Then the increase in area of the garden,

→ 11.664 - 8.1

→ 3.564 m²

Hence, 3.564 m² is the increase in area.

Alonzo finish history assignment and 5/8 hours then he completed his math assignment and 1/3 hours what was the total amount of time allowed to spend doing these two assignments

Answers

Step-by-step explanation:

The answer is 5/8 + 1/3

Answer = 5*3 /(8*3) +8/24 =23/24

Answer = 23/24

Consider the following data representing the price of refrigerators (in dollars).14051405, 11211121, 13391339, 10961096, 12991299, 14011401, 11381138, 11491149, 12231223, 10711071, 13991399, 14001400, 12421242, 13181318, 11011101, 10651065, 14281428, 12251225, 13501350, 13581358, 13121312Copy DataPrice of Refrigerators (in Dollars)Class Frequency Class Boundaries Midpoint Relative Frequency Cumulative Frequency1049–1118 1119–1188 1189–1258 1259–1328 1329–1398 1399–1468 Step 2 of 7 : Determine the frequency of the fifth class.

Answers

Answer:

3

Step-by-step explanation:

Given the data:

1405, 1121, 1339, 1096, 1299, 1401, 1138, 1149, 1223, 1071, 1399, 1400, 1242, 1318, 1101, 1065, 1428, 1225, 1350, 1358, 1312

Using the intervals:

Class interval ___ Frequency

1049–1118 ________ 4

1119–1188 ________ 3

1189–1258 ________3

1259–1328 _______ 3

1329–1398 _______ 3

1399–1468 _______ 5

From the table ; the fifth class is the interval :

1329 - 1398 and it has a frequency of 3

The administration conducted a survey to determine the proportion of students who ride a bike to campus. Of the 123 students surveyed 5 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.

a. The sample needs to be random but we don’t know if it is.
b. The actual count of bike riders is too small.
c. The actual count of those who do not ride a bike to campus is too small.
d. n*^p is not greater than 10.
e. n*(1−^p)is not greater than 10.

Answers

Answer:

b. The actual count of bike riders is too small.

d. n*p is not greater than 10.

Step-by-step explanation:

Confidence interval for a proportion:

To be possible to build a confidence interval for a proportion, the sample needs to have at least 10 successes, that is, [tex]np \geq 10[/tex] and at least 10 failures, that is, [tex]n(1-p) \geq 10[/tex]

Of the 123 students surveyed 5 ride a bike to campus.

Less than 10 successes, that is:

The actual count of bike riders is too small, or [tex]np < 10[/tex], and thus, options b and d are correct.

4 people take 3 hours to paint a fence assume that all people paint at the same rate How long would it take one of these people to paint the same fence?​

Answers

Answer:

12

Step-by-step explanation:

What is the cardinal number of the set {-1,3,7,52,36,19,-6}

Answers

Answer:

can you please send me another one

A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?

Answers

Answer:

10:3

Step-by-step explanation:

Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.

For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.

So make 5/2 to a 10/4.

Take the numerator 10 & 3.

Your answer will be 10:3

No problem.

find and sketch the domain of the function. f(x,y)=√(4-x^2-y^2) +√(1-x^2)

Answers

Answer:

Hello

Step-by-step explanation:

The domain is limited with 2 lines parallel: -1 ≤ x ≤ 1

and the disk ? (inside of a circle) of center (0,0) and radius 2

[tex]dom\ f(x,y)=\{(x,y) \in \mathbb{R} ^2 | \ -1\leq x \leq -1\ and \ ( -\sqrt{4-x^2} \leq \ y \leq \sqrt{4-x^2}\ ) \ \}\\[/tex]

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