Approximately 1.65 million high school students take the Scholastic Aptitude Test (SAT) each year and nearly 80% of the college and universities without open admissions policies use SAT scores in making admission decisions (College Board, March 2009). The current version of the SAT includes three parts: reading comprehension, mathematics, and writing. A perfect combined score for all three parts is 2400. A sample of SAT scores for the combined three-part SAT are as follows:
1665 1275 1650 1590 1475 1490
1525 2135 1560 1880 1680 1560
1355 1280 1150 1420 14409 4016
4510 6014 8517 5512 6013 9017
8015 8519 901 3751 7301 1755
Required:
a. Show a frequency distribution and histogram. Begin with the first class starting at 800 and use a class width of 200.
b. Comment on the shape of the distribution.
c. What other observations can be made about the SAT scores based on the tabular and graphical summaries?
Answers
Answer:
Step-by-step explanation:
Hello!
The sample shows the scores for the combined three-part SAT.
Raw data in first attachment.
a.
To arrange the data in a frequency table using class intervals you have to determine the number of intervals you want to use and calculate their width. In this case, the width is given and so is the lower limit of the first interval, you calculate the successive limits by adding the width. The lower limit of the next interval will be the upper limit of the previous one:
1) 800 + 200= 100
First interval [800; 1000)
2) 1000 + 200
Second interval
[1000; 1200)
And so on until you reach the maximum value of the data set,
[1200; 1400)
[1400; 1600)
[1600; 1800)
[1800; 2000)
[2000; 2200)
Then you have to order the data from least to greatest and count how many observations correspond to each value, this way you'll determine the observed frequency for each interval.
Table and histogram in second attachment.
b.
As you can see in the histogram, this distribution is symmetrical centered in the interval [1400; 1600) and there are no outliers observed.
c.
Values around 1400-1600 are the most common ones while scores around 800-1000 or 2000-2200 are more uncommon, in this sample it seems the probability to obtain a perfect score for the combined three-part SAT is extremely low.
I hope you have a nice day!
Related Questions
Solve seven square root three plus two square root nine and explain whether the answer is rational or irrational
Answers
Answer:
Step-by-step explanation:
5
The square of a number is 12 less than 7 times the number.what is the number?
Answers
Answer:
n = 3 or n = 4
Step-by-step explanation:
Let the unknown number be n.
Then:
n² = 7n - 12
In standard quadratic form, we have:
n² - 7n + 12 = 0
In factored form, we have:
(n - 3)(n - 4) = 0, and so
n = 3 and n = 4
The average score Josie had in 6 subjects is 72 and her average score after 2 additional subjects were added is 74.25. If she scored 80 in the 7th subject, what was her score in the 8th subject correct to the nearest whole number?
Answers
Answer:82
Step-by-step explanation:
a+b+c+d+e+f/6=72
a+b+c+d+e+f=6*72
a+b+c+d+e+f=432
a+b+c+d+e+f+g+h/8=74.25
a+b+c+d+e+f+g+h=594
g=80
h=?
432+80+h=594
512+h=594
h=82
hope it helps brainleast plz...
Account A and Account B both have a principal of $2,000 and an annual interest rate of 5%. No additional deposits or withdrawals are made. Account A earns simple interest. Account B earns interest compounded annually. Compare the amounts in the two accounts after 20 years. Which earns more interest? How much more?
Answers
Answer:
Which earns more interest = Account B
How much more = $1,306.60
Step-by-step explanation:
Given;
Principal P = $2,000
Interest rate r = 5% = 0.05
Time t = 20 years
For account A;
Simple interest = P×r×t
Substituting the values;
Simple interest = 2,000 × 0.05 × 20 = $2000
Interest on account A = $2,000
For account B;
Compound interest
Final amount = P(1 + r)^t
Since it's compounded annually
Substituting the values;
Final amount = 2000(1+0.05)^20
Final amount = $5306.60
Interest = final amount - principal = $5306.60 -$2000
Interest = $3,306.60
Therefore, account B earns more interest.
Difference = account B interest - account A interest
Difference = $3,306.60 - $2,000
Difference = $1,306.60
An AP news service story, printed in the Gainesville Sun on May 20, 1979, states the following with regard to debris from Skylab striking someone on the ground: "The odds are 1 in 150 that a piece of Skylab will hit someone. But 4 billion people ... live in the zone in which pieces could fall. So any one person’s chances of being struck are one in 150 times 4 billion—or one in 600 billion." Do you see any inaccuracies in this reasoning?
Answers
Answer:
The odds are one in approximately 27 million.Not one in 600 billionStep-by-step explanation:
From the news story, we are told that:
The odds are 1 in 150 that a piece of Skylab will hit someone.
However, 4 billion people live in the zone in which pieces could fall.
Therefore, any one person’s chances of being struck are:
[tex]=\dfrac{1}{150} \times 4$ billion\\=\dfrac{1}{37.5}$ billion\\\\=26,666,667 million[/tex]
Therefore, the odds are one in approximately 27 million.
The inaccuracy presented in this reasoning was that the odds are one in 600 billion.
Explain how to find the range of a data set. Choose the correct answer below. A. The range is found by subtracting the first data entry from the last data entry. B. The range is found by adding the first and last data entries. C. The range is found by subtracting the minimum data entry from the maximum data entry. D. The range is found by adding the minimum and maximum data entries.
Answers
Answer:
C
Step-by-step explanation:
The range of a data set is the difference between the biggest and smallest values, so to find it, you just subtract the minimum from the maximum.
Round the following number to the nearest thousand 2385
Answers
By rounding of the following number to the nearest thousand is 2000.
What is rounding a number to some specific place?Rounding some number to a specific value is making its value simpler (therefore losing accuracy), mostly done for better readability or accessibility.
'
Rounding to some place keeps it accurate on the left side of that place but rounded or sort of like trimmed from the right in terms of exact digits.
Round the following number to the nearest thousand
2385
= 2000
Thus, by rounding of the following number to the nearest thousand is 2000.
Learn more about rounding numbers here:
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Please answer this correctly
Answers
Answer:
1.5 meters
Step-by-step explanation:
The formula for the area of a trapezoid is h * (a+b)/2, where a is the first base and b is the second base. Now, we can work backwards to determine the height of the trapezoid:
3.75=h*(1.7+3.3)/2
3.75=h*2.5
h=3.75/2.5=1.5
Hope this helps!
Answer:
Step-by-step explanation:
use the formula and rearrange for h.
1/2 x h x (a + b) = A
1/2 x (1.7 + 3.3) x h = 3.75
2.5 x h = 3.75
h = 1.5
hope this helps! :)
Explain what the number 0 on the gauge represents and explain what the numbers above 0 represent
Answers
Do all perpendicular lines have negative reciprocal slopes?
Answers
Not necessarily, the more correct definition is opposite reciprocal slopes.
The example used is how horizontal and vertical lines are parallel. Horizontal lines have a slope of 0, also written as 0/1. However, vertical lines have an undefined slope, which isn't necessarily negative. It has a slope of 1/0, which is undefined. In this case, the reciprocal isn't negative.
In all other cases (1 and -1, 2 and -1/2, etc.) yes, the perpendicular pairs are negative and reciprocal.
List the important features for the graph of a quadratic function.
Answers
Answer:
VertexMinimum PointMaximum PointRootsAxis of SymmetryStep-by-step explanation:
The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.
The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.
The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.
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The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The important features for the graph of a quadratic function will be
The parabola is symmetric about the line which is passing through focus.
The quadratic function can be expressed in the form of vertex form.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
More about the quadratic equation link is given below.
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for each sequence find the first 4 terms and the 10th term n+5 , , , , ...,
Answers
Answer:
10,15.20.25
Step-by-step explanation:
+5 in each number
Please help. I’ll mark you as brainliest if correct!
Answers
Answer:
a= -3/8
b= 1/8
Step-by-step explanation:
To remove i from the denominator, we need to multiply the numerator and denominator by -i
[tex]\frac{(-1-3i)(-i)}{8i(-i)}[/tex]
This simplifies to
[tex]\frac{i+3i^{2} }{-8i^{2} }[/tex]
This further simplifies to
[tex]\frac{i-3}{8}[/tex]
This can be rewritten as
[tex]-\frac{3}{8} +\frac{1}{8} i[/tex]
a= -3/8
b= 1/8
Answer:
[tex] a = - \frac{3}{8} \\ \\ b = \frac{1}{8} [/tex]
Step-by-step explanation:
[tex] \frac{ - 1 - 3i}{8i} \\ \\ = \frac{ - 1 - 3i}{8i} \times \frac{i}{i} \\ \\ = \frac{( - 1 - 3i)i}{8i \times i} \\ \\ = \frac{ -1 \times i - 3 {i}^{2} }{8 {i}^{2} } \\ \\ = \frac{ - i - 3 ( - 1)}{8 ( - 1) } \\ \\ = \frac{ - i + 3}{ - 8} \\ \\ = \frac{ i - 3}{ 8} \\ \\ = \frac{ - 3 + i}{ 8} \\ \\ = \frac{ - 3}{8} + \frac{i}{8} \\ \\ \purple{ \bold{ = - \frac{3}{8} + \frac{1}{8} i}} \\ equating \: it \: with \: a + bi \\ \\ a = - \frac{3}{8} \\ \\ b = \frac{1}{8} \\ [/tex]
A random sample of 150 mortgages in the state of Florida was randomly selected. From this sample, 17 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is ________.
Answers
Answer:
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 150, \pi = \frac{17}{150} = 0.1133[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 - 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.0531[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.1133 + 2.327\sqrt{\frac{0.1133*0.8867}{150}} = 0.1735[/tex]
The 98% confidence interval for the proportion based on this sample is (0.0531, 0.1735).
The article "A Shovel with a perforated blade reduces energy expenditure required for digging wet clay" (Human Factors, 2010:492-502) reported on an experiment in which each of 13 workers was provided with both a conventional shovel and a shovel whose blade was perforated with small holes. The authors of the cited article provided the following data on stable energy expenditure (measured in kilocalories per kg of subject per pounds of clay):
1 2 3 4 5 6 7 8 9 10 11 12 13 Worker Conventional 0.0011 0.0014 0.0018 0.0022 0.001 0.0016 0.0028 0.002 0.0015 0.0023 0.0017 0.002 0.0014 Perforated 0.0011 0.001 0.0019 0.0013 0.0011 0.0017 0.0024 0.002 0.0013 0.0017 0.002 0.0013 0.0013 Carry out a test of hypotheses at significance level 0.05 to see whether the true average energy expenditure using the conventional shovel exceeds that using the perforated shovel. (hint: this is a paired-design!). Make sure to calculate a p-value!
Answers
Answer:
Step-by-step explanation:
Corresponding true average energy expenditure of shovel with conventional blade and true average energy expenditure of shovel with perforated blades form matched pairs.
The data for the test are the differences between the true average energy expenditures of the shovels.
μd = true average energy expenditure of shovel with conventional blade minus true average energy expenditure of shovel with perforated blades.
Conventional perforated diff
0.0011 0.0011 0
0.0014 0.0010 0.0004
0.0018 0.0019 -0.0001
0.0022 0.0013 0.0009
0.0010 0.0011 -0.0001
0.0016 0.0017 -0.0001
0.0028 0.0024 0.0004
0.0020 0.002 0
0.0015 0.0013 0.0002
0.0023 0.0017 0.0006
0.0017 0.002 -0.0003
0.0020 0.0013 0.0007
0.0014 0.0013 0.0001
Sample mean, xd
= (0 + 0.0004 - 0.0001 + 0.0009 - 0.0001 - 0.0001 + 0.0004 + 0 + 0.0002 + 0.0006 - 0.0003 + 0.0007 + 0.0001)/13 = 0.0002077
xd = 0.0002077
Standard deviation = √(summation(x - mean)²/n
n = 13
Summation(x - mean)² = (0 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2+ (0.0009 - 0.0002077)^2 + (- 0.0001 - 0.0002077)^2 + ( - 0.0001 - 0.0002077)^2 + (0.0004 - 0.0002077)^2 + (0 - 0.0002077)^2 + (0.0002 - 0.0002077)^2 + (0.0006 - 0.0002077)^2 + (- 0.0003 - 0.0002077)^2 + (0.0007 - 0.0002077)^2 + (0.0001 - 0.0002077)^2 = 0.00000158923
Standard deviation = √(0.00000158923/13
sd = 0.00035
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 13 - 1 = 12
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (0.0002077 - 0)/(0.00035/√13)
t = 2.14
We would determine the probability value by using the t test calculator.
p = 0.027
Since alpha, 0.05 > than the p value, 0.027, then we would reject the null hypothesis. Therefore, at 5% significance level, we can conclude that the true average energy expenditure using the conventional shovel does not exceed that using the perforated shovel.
The total claim amount for a health insurance policy follows a distribution with density function 1 ( /1000) ( ) 1000 x fx e− = , x > 0. The premium for the policy is set at the expected total claim amount plus 100. If 100 policies are sold, calculate the approximate probability that the insurance company will have claims exceeding the premiums collected.
Answers
Answer:
the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Step-by-step explanation:
The probability of the density function of the total claim amount for the health insurance policy is given as :
[tex]f_x(x) = \dfrac{1}{1000}e^{\frac{-x}{1000}}, \ x> 0[/tex]
Thus, the expected total claim amount [tex]\mu[/tex] = 1000
The variance of the total claim amount [tex]\sigma ^2 = 1000^2[/tex]
However; the premium for the policy is set at the expected total claim amount plus 100. i.e (1000+100) = 1100
To determine the approximate probability that the insurance company will have claims exceeding the premiums collected if 100 policies are sold; we have :
P(X > 1100 n )
where n = numbers of premium sold
[tex]P (X> 1100n) = P (\dfrac{X - n \mu}{\sqrt{n \sigma ^2 }}> \dfrac{1100n - n \mu }{\sqrt{n \sigma^2}})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{\sqrt{n}(1100-1000}{1000})[/tex]
[tex]P(X>1100n) = P(Z> \dfrac{10*100}{1000})[/tex]
[tex]P(X>1100n) = P(Z> 1) \\ \\ P(X>1100n) = 1-P ( Z \leq 1) \\ \\ P(X>1100n) =1- 0.841345[/tex]
[tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Therefore: the approximate probability that the insurance company will have claims exceeding the premiums collected is [tex]\mathbf{P(X>1100n) = 0.158655}[/tex]
Write the product in standard form.
(2 - 3i)(2 + i)
Answers
Answer:
Brainelist?
Step-by-step explanation:
7-4i
just use a online calculator
Answer:
7-4i
Step-by-step explanation:
(2 - 3i)(2 + i)
FOIL
first 2*2 = 4
Outer: 2i
Inner: -3i*2 = -6i
Last: -3i*i = -3i^2 = -3(-1) = 3
Add them together
4+2i-6i+3
7-4i
Complete the point- slope equation of the line through (8, -8 and (9, 8). Y - 8 =
Answers
What is the solution? X/12+3< or = 7
Answers
Answer:
x <= 48
Step-by-step explanation:
Subtract 3 from both sides
x/12 <= 4
Multiply by 12
x <= 48
find the equation ( in form of y = mx+c) of line which has a gradient of -3 and a y intercept of -2
Answers
Answer:
The answer is y = -3x - 2.
Step-by-step explanation:
Given that in slope-form equation, m represents gradient and c is y-intercept. So you have to sbustitute the values into the equation :
[tex]y = mx + c[/tex]
[tex]let \: m = - 3 \\ let \: c = - 2[/tex]
[tex]y = - 3x - 2[/tex]
What is equal to 5x when x is equal 50
Answers
If X=50 then you would do 5x50=250
Answer:
250
Step-by-step explanation:
if x=50
5(x)=5*50=250
Hope it helps..Pls mark as Brainliest!!
A company makes candles in the shape of a right cone. The lateral surface of each candle is covered with paper for shipping and each candle also has a plastic circular base. Find the amount of paper needed to cover the lateral surface of each candle. Then find the total amount of paper and plastic needed for the candle. Round to the nearest tenth. Use 3.14 for π.
Answers
Answer:
If we have a cone-shape candle with r=2 cm and h=3 cm, then the amount of paper needed is 18.84 cm^2 and the amount of plastic needed is 12.56 cm^2.
Step-by-step explanation:
The question is incomplete: no numerical values for the dimensions of the cone are given.
A right cone is defined by the radius r of the base and the height h.
The base area is the area of a circle with radius r:
[tex]A_b=\pi r^2[/tex]
The lateral area is calculated as:
[tex]A_l=\pi \cdot r\cdot l[/tex]
As the values for r and h are not given, we will use an example with r=2 and h=3.
Then, the amount of paper needed is:
[tex]A_l=\pi \cdot r\cdot l=3.14\cdot (2\,cm)\cdot (3\, cm)=18.84\,cm^2[/tex]
The amount of plastic needed is:
[tex]A_b=\pi r^2=3.14\cdot (2\,cm)^2=3.14\cdot 4\,cm^2=12.56\,cm^2[/tex]
Can someone help me?
Answers
Answer:
Step-by-step explanation:
a)4a-6a d)2x+4y-10x
=-2a. =-8-+4y
b)14-1-10
=3
c)2+8
=10
e)answer is 6 x raised to the power 3
f)7x raised to the power 2-5x-y
help as quick as possible 18 points :)
Answers
Answer:
Step-by-step explanation:
1/10*5 is the answer i think...
Which table represents a linear function?
Answers
Answer:
Top right option
Step-by-step explanation:
Solve.
3^x+1 = 9^ 5x
a. x=3
b. x = 1/3
c. x=9
d. x= 1/9
Answers
Answer:
x = 1/9
Step-by-step explanation:
3^ (x+1) = 9 ^ (5x)
Replace 9 with 3^2
3^ (x+1) = 3^2 ^ (5x)
We know that a^b^c = a ^(b*c)
3^ (x+1) = 3^(2 * (5x))
3^ (x+1) = 3^(10x)
The bases are the same so the exponents are the same
x+1 = 10x
Subtract x from each side
x+1-x = 10x-x
1 = 9x
Divide each side by 9
1/9 = 9x/9
1/9 =x
2/5 plus 1/4 plus 7/10
Answers
The answer is 1 7/20
2/5 x 4/4 + 7/10 x 2/2 + 1/4 x 5/5
= 8/20 + 14/20 + 5/20
= 27/20
= 1 7/20
Answer:
27/20 or 1 and 7/20
Step-by-step explanation:
All you do is find common factors.
4 lines are shown. A line with points A, F, D intersects with a line with points B, F, E at point F. A line extends from point F to point G between angle E F D. Another line extends from point F to point D in between angle B F D. In the diagram, which angle is part of a linear pair and part of a vertical pair? AngleBFC AngleCFG AngleGFD AngleEFA
Answers
Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
What are linear pair and part of a vertical pair?If two angles is said to create a linear pair, the angles are then regarded as supplementary and it is said that their measures often add up to 180°.
Note that Vertical angles are said to be pair of nonadjacent angles created by the crossing or the intersection of any two straight lines.
Since vertical angles are seen if "X" created by two straight lines then when you look at the image attached, you can see that the angle that can from this is Angle EFA.
Therefore, Based on the above, the angle that is said to be a part of a linear pair and part of a vertical pair is Angle EFA.
Learn more about vertical pair from
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Express the following in usual form
Answers
Answer:
52300
Step-by-step explanation:
When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300
Marta recorded the temperature at 8 p.m. as 56°F and the temperature at 8 a.m. the next morning as 36°F. Marta assumed the temperature changed at a constant rate. She wrote an equation to find the number of degrees the temperature dropped each hour, h, of the night. Which equation did Marta write?
Answers
Answer: 5h/3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21
Answer:
5h 3
Step-by-step explanation:
12 hours passed, and 20 degrees dropped.
Every hour, that's 20/12 = 5/3 degrees dropped. Therefore, the equation is 5h/3.
Hope that helped,
-sirswagger21