Answer:
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Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is approximately normal with a mean of 500 and a standard deviation of 100. Rubin takes the ACT math exam and scores 31 on the math portion. ACT scores are approximately normally distributed with a mean of 18 and a standard deviation of 6.7
(a) Relative to their peers who also took the tests, who performed better on his test? Explain.
(b) A certain school will only consider those students who score in the top 1% in the math section. What grades would Ronald and Rubin have to receive on their respective tests to be considered for admission?
(c) Between what two grades does 95% of the population fall for the ACT and the SAT exams?
Answer:
a) Due to the higher z-score, Ronald performed better relative to his peers on the test.
b) Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.
c) 95% of the population fall between graded of 4.868 and 31.132 on the ACT.
95% of the population fall between graded of 304 and 696 on the SAT.
Step-by-step explanation:
Normal probability distribution
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question:
(a) Relative to their peers who also took the tests, who performed better on his test? Explain.
We have to find whoever has the higher z-score.
Ronald:
Ronald scores 700 on the math section of the SAT exam. The distribution of SAT scores is approximately normal with a mean of 500 and a standard deviation of 100. So the z-score is found when [tex]X = 700, \mu = 500, \sigma = 100[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 500}{100}[/tex]
[tex]Z = 2[/tex]
Rubin:
Rubin takes the ACT math exam and scores 31 on the math portion. ACT scores are approximately normally distributed with a mean of 18 and a standard deviation of 6.7. So the z-score is found when [tex]X = 31, \mu = 18, \sigma = 6.7[/tex]. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{31 - 18}{6.7}[/tex]
[tex]Z = 1.94[/tex]
Due to the higher z-score, Ronald performed better relative to his peers on the test.
(b) A certain school will only consider those students who score in the top 1% in the math section. What grades would Ronald and Rubin have to receive on their respective tests to be considered for admission?
They have to be in the 100 - 1 = 99th percentile, that is, they need a z-score with a pvalue of at least 0.99. So we need to find for them X when Z = 2.325.
Ronald:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.325 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = 232.5[/tex]
[tex]X = 732.5[/tex]
Rubin:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]2.325 = \frac{X - 18}{6.7}[/tex]
[tex]X - 18 = 15.58[/tex]
[tex]X = 33.58[/tex]
Ronald needed a grade of at least 732.5, and Rubin of at least 33.58.
(c) Between what two grades does 95% of the population fall for the ACT and the SAT exams?
They fall between the 100 - (95/2) = 2.5th percentile and the 100 + (95/2) = 97.5th percentile, that is, they fall between X when Z = -1.96 and X when Z = 1.96.
ACT:
Lower bound:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 18}{6.7}[/tex]
[tex]X - 18 = -1.96*6.7[/tex]
[tex]X = 4.868[/tex]
Upper bound:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 18}{6.7}[/tex]
[tex]X - 18 = 1.96*6.7[/tex]
[tex]X = 31.132[/tex]
95% of the population fall between graded of 4.868 and 31.132 on the ACT.
SAT:
Lower bound:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.96 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = -196[/tex]
[tex]X = 304[/tex]
Upper bound:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = 196[/tex]
[tex]X = 696[/tex]
95% of the population fall between graded of 304 and 696 on the SAT.
11/20
A box contains 5 red marbles, 6 white marbles, and 4 blue marbles. Find
P(red or blue)
Answer: 3/5
Step-by-step explanation:
Probability is the number of favorable outcomes divided by the total number of outcomes. In this case, there are 5+4+6, or 15, possible outcomes, because there is one selection from 15 marbles. Therefore, the probability of choosing a blue marble is 4/15, and the probability of choosing a red marble is 5/15. Add these together to get the probability of choosing a red or blue marble:
(4/15)+(5/15)=9/15
9/15 simplifies to 3/5.
I will give brainiest to whoever answers correctly !!
Answer:
14.0
Step-by-step explanation:
14.096 rounded to the nearest tenth
Write each fraction as a decimal
3 15/44
HELP IOLL MARK U BRAINLIEST I SWEAR
Answer:
You aren't posting pictures
Step-by-step explanation:
Sam found a wrecked car that could she could fix. She bought the car for
65% of the original price of $7200. What did she pay for the car? SHOW YOUR WORK
$11,076.92
$4,680
$2,520
$468
=======================================================
Work Shown:
x% = x/100
65% = 65/100 = 0.65
So 65% in decimal form is 0.65
We use this to find the amount Sam paid for the car
65% of 7200 = 0.65*7200 = 4,680 dollars
--------------
Here's an alternative way to show your work
part/whole = percent/100
x/7200 = 65/100
x/7200 = 0.65
x = 0.65*7200
x = 4680
Ultimately we end up with 0.65*7200 and that's how we lead to the same answer as before. You could cross multiply like so
x/7200 = 65/100
x*100 = 7200*65
100x = 468000
x = 468000/100
x = 4680
So there are many paths to the same answer.
There is a $30 fee to rent a tool from Jeff’s Tool Rentals plus $6 per day. If Hector rents a jackhammer for 5 days, what is his total bill?
Answer: 60$
Step-by-step explanation:
because you have the initial 30$ One time fee then you times 6$ by 5 days and 6x5= 30 then you add 30+30= 60
Find the value of each variable.
What is the area of this figure? 7 km 6 km 12 km 4 km 4 km 5 km 3 km 3 km
The area of figure will be;
⇒ 105.56 km²
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The figure is shown.
Now,
The area of figure is find as;
Total area = (12 × 7) + (π × 4² / 4) + (3 × 3)
= 84 + 3.14 × 4 + 9
= 93 + 12.56
= 105.56 km²
Thus, The area of figure will be;
⇒ 105.56 km²
Learn more about the area visit:
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Plz help I’ll give Brainly
Answer:
[i] Area of Juan's garden:
Soln,
length(l)=16
width(w)=12
area(a)=?
Now,
a=l×w
=16×12
=192
[ii] Area of Matthew's garden:
Soln,
length(l)=18
width(w)=21
area(a)=?
Now,
a=l×w
=18×21
=378
So,the area ofJuan's garden=192
And
the area of Matthew's garden=378
Is 3/9 more less or equal to 5/8
Answer:
less
Step-by-step explanation:
Answer:
3/9 is less that 5/8
Step-by-step explanation:
To answer this question we can simply infer which is greater by using simple knowledge.
We know that 1/9 and 1/8 are both relatively small parts of a whole.
Now we know that 1/8 is greater than 1/9
If we think about it 5/8 is bound to be greater than 3/9 because the parts of a whole when you are dealing with 8ths are greater than when you are dealing with 9ths and since there are more 8ths than 9ths in the comparison as in (3 < 9) then we should already know that:
5/8 is greater than 3/9
Last year, a stereo system sold for $450. This year, it sold for $382.50. What is the percent of change from last year to this year?
U
+
X
с
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Answer:
15% decrease
382.50-450 divided by 450 times 100
Put the following equation and slope intercept form: y-2= 1/7(x-3) pls help
Answer:
y=1/7x+11/7
Step-by-step explanation:
I used mathaway
All flour from five bags with 3/8 lbs of flour in each was divided into equal parts to make 7 loaves of bread. How can you calculate the amount of flour used for each loaf? select all that apply
was divided into equal parts to make 7 loaves of bread. How can you mount of flour used for each loaf? select all that apply
Step-by-step explanation:
Answer:
B, C, F
Step-by-step explanation:
C = 3/8 divided 7 times 5. 3/8 lbs of flour in each was divided into equal parts to make 7 loaves. 3/8 divide by 7. Since there are 5 bags, times 5.
B = 3/8 times (for the five bags) times 5 divided by 7 samething from C.
F = You know the pattern now. Hint: B is the answer...
What is the period of y= sec X?
Given:
The given function is
[tex]y=\sec x[/tex]
To find:
The period of given function.
Solution:
General sec function is defined as
[tex]y=A\sec (Bx+C)+D[/tex]
Where, A is amplitude, [tex]\dfrac{2\pi}{B}[/tex] is period, [tex]-\dfrac{C}{B}[/tex] is phase shift and D is vertical shift.
We have,
[tex]y=\sec x[/tex]
Here, B=1. So,
[tex]Period=\dfrac{2\pi}{1}[/tex]
[tex]Period=2\pi[/tex]
Therefore, the period of given function is 2π.
The value of period of function y = sec x is, 2π.
The given function is,
y = sec x
Since, We know that,
General form of equation for sec x is,
y = A sec (Bx + C) + D
Where, A is amplitude, 2π/B is period and D is vertical shift.
Here, function is,
y = sec x
Hence, B = 1,
So, Period = 2π/B
= 2π/1
= 2π
Thus, The value of period of function y = sec x is, 2π.
Learn more about trigonometric ratios at:
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tim's piggy bank contains nickels and quarters worth $12.45. he has 69 coins in all. how many of each coins does he have?
Answer: There can be multiple combos.
Sam's Fruit Cellar earns a $0.40 profit for each apple that it sells and a $0.40 profit for each banana that it sells. Which expression(s) show(s) Sam's total
profits from selling apples (a) and bananas (b)? Select all that apply.
*00.40(ab)
*0 0.80(a + b)
*0.80(ab)
*0.40a+ 0.40b
*0.40(a + b)
*0.40+ a +0.40 + b
Answer:
0.40a+ 0.40b 0.40(a + b)Step-by-step explanation:
If a apples sold then profit is:
0.40aIf b bananas sold then profit is:
0.40bTotal profit is the sum of the profits:
0.40a + 0.40bCorrect options are D and E ( or 4 and 5)
how do you create a graph for linear equation? I need to graph 3x=4
Answer:
Look at the graph below, hope this helped.
Step-by-step explanation:
Use the theorem part 1
Answer:
(a)
Step-by-step explanation:
The base angles theorem states that if 2 sides of a triangle are congruent, that is an isosceles triangle then the angles opposite these sides are equal.
Answer:
a) Base Angle TheoremStep-by-step explanation:
The Base Angle Theorem states that in an isosceles triangle, the angles opposite the congruent sides are congruent.
using partial quotients 5,166 divide by 42
Answer: 123
Step-by-step explanation:
I will give brainiest to whoever answers correctly !!
Replace x with 10.
The exponent is now 0.1(10) = 1
Now you have 5000(1.181)^1
1.181^1 = 1.181
So now 5000 x 1.181 = 5,905
The answer is 5,905
How do the values compare? Order the values from least to greatest. 1/2 , 2 , 2 1/2 , -1/2 , 1 1/2 , 2 1/2
Answer:
First always the positive is greater than the negative
Then 1/2, 2, 21/2, 2, 11/2 are greater than - 1/2
1/2=0.5
21/2=10.5
11/2=5.5
Then from lowest to greatest
-1/2,1/2,2,11/2,21/2
I hope you understand
Find the missing length.
C =
✓ [?]
C
7
9
Pythagorean Theorem: a2 + b2 = c2
Enter
Answer:
c = √130
Step-by-step explanation:
Using Pythagorean theorem, c² = a² + b².
Where,
a = 9
b = 7
c = hypotenuse = ??
Thus:
c² = 9² + 7²
c² = 130
c = √130
what is the best approximation for the circumference of a circle with a daimeter of 300 ft use 3.14 approximation pi
Answer: 942
Step-by-step explanation:
so your d is 300 so your r = 300/2= 150
a=3.14*r*r= 3.14*150*150= 70650
c= 3.14*d= 3.14*300= 942
Can someone please explain how I apply SOHCAHTOA properly to this?
Answer:
e
Step-by-step explanation:
It takes Ty 4 hours 30 minutes to read his favorite book, reading at a constant rate of 100 pages
every 50 minutes. How many pages are in Ty's favorite book?
Answer:
540 pages
Step-by-step explanation:
100 pages = 50 mins
??? pages = 270 mins (converted 4hrs 30 mins to minutes)
Now you could cross multiply to find what the number of pages are:
100 pages x 270 mins = 50 mins x ??? pages
27000 = 50 mins x ??? pages
27000/50 = ??? pages
540 = ??? pages
So there are 540 pages in his favourite book.
Pls help extra points and mark brainlist
Answer:
In order from top to bottom: 5^2, 125, 50
Step-by-step explanation:
1. (3+2) × 5 = 5 × 5 = 5^2
2. 5^3 = 5 × 5 × 5 = 125
3. 10^2 / 2 = 100/2 = 50
Answer:
10^2/2=50
5^3=125
(3+2)*5=5^2
Step-by-step explanation:
A company is allowed to interview candidates until two qualified candidates are found. But budget constraints dictate that no more than 10 candidates can be interviewed. List the sample space.
Answer:
Kindly check attached picture for sample space design
45 ways
Step-by-step explanation:
Number of qualified candidates to be chosen = 2
Number of candidates to be interviewed = 10
Combination formula :
nCr = n! / (n-r)! r!
10C2 = 10! ÷ (10 - 2)!2!
10C2 = 10*9 / 2 * 1
10C2 = 90/2
10C2 = 45 different samples
Our sample space will contain 45 different samples
Bananas sell for $0.44 pounds. How much will 6 pounds of bananas cost.
Answer:
$2.64
Step-by-step explanation:
0.44 times 6.
Answer:
2.64
Step-by-step explanation:
6*0.44=2.64
i hope it will help you
The lunch at Dion's Place has choice of ham, turkey, or roast beef on rye or white bread white juice, milk, or tea.
A. How many different lunches are possible.
B. What is the probability that the lunch special of the day is ham on rye with tea?
Please Help With Both Answers - I Will Give BRAINLIEST, and 50 points.
Total combinations are found by multiplying the quantities of each part by each other.
3 kinds of meat x 2 types of bread x 3 types of drinks
A) total combinations = 3 x 2 x 3 = 18
B) there are 18 different combinations, ham in rye with tea is 1 combination.
The probability would be 1/18