Let X be the percentage score on a college-entrance exam for students who did not participate in an exam-preparation seminar. X is modeled by a uniform distribution on [a,100]. Let Y be the percentage score on a college-entrance exam for students who did participate in an exam-preparation seminar. Y is modeled by a uniform distribution on [1.25a,100]. It is given that E[X^2] = 19,600/3.Calculate the 80th percentile of Y. A. 80 B. 85 С. 90 D. 92 E. 95

Answers

Answer 1

Answer:

E. 95

Step-by-step explanation:

[tex]\text{Given that:} \\ \\ X \sim U(a,100) \\ \\ fx(x) = \dfrac{1}{100-a} \\ \\ E[X^2] = \int _x f_x (x) \ dx \\ \\ \implies \int^{100}_{a} \dfrac{x^2}{100-a}dx \\ \\ =\dfrac{100^3-a^3}{3(100-a)} \\ \\ =\dfrac{100^2+100a+a^2}{3} \\ \\ E[X^2] = \dfrac{19600}{3}=\dfrac{100^2+100a+a^2}{3} \\ \\\implies a^2 +100a+10000=19600 \\ \\ \implies a^2 +100a -9600 = 0 \\ \\ \implies a = \dfrac{-100 \pm \sqrt{100^2 -4(-9600)} }{2} \\ \\=\dfrac{-100 \pm \sqrt{48400}} {2} \\ \\ = \dfrac{-100 \pm 220}{2} \\= 60 \ OR \ 160[/tex]

[tex]\text{SInce X is a percentage score on an exam }\ P(X \ge 0) = 1 \text{which means } \ a = 60\\ \\Y \sim U (1.25a,100) = U(75,100)\\ \\ f_y(y) = \dfrac{1}{100-75} = \dfrac{1}{25} \\ \\ \text{Let assume the 80th percentile of Y be} \ y_{80} } \\ \\ \\Then; \ P(Y \le y_{80}) =80\% \implies \int^{y_{80}}_{75} \ f_Y (y) \ dy = 0.8 \\ \\ \implies \int^{y_{80}}_{75}\dfrac{1}{25} \ dy = 0.8 \\ \\ \implies \dfrac{y_{80}-75}{25}= 0.8 \\ \\ \implies y_{80} = 95[/tex]


Related Questions

0.2 as a fraction (out of 100)

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Answer =2/1000

Step-by-step-explanation

Suppose you know that 10% of 250 is 25. How could you use
that information to find 30% of 250?

Answers

Answer:

triple the answer

Step-by-step explanation:

.1×250=25

.3×250= 75

25×3=75

what is the value of y? ​

Answers

9514 1404 393

Answer:

  y = 8√3

Step-by-step explanation:

In the 30°-60°-90° "special" triangle, the ratio of sides lengths is ...

  1 : √3 : 2 = 8 : y : hypotenuse

In order for these ratios to be equal, we must have ...

  y = 8√3

__

If you want to solve this using your trig skills, you recognize that ...

  Tan = Opposite/Adjacent

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  y = 8√3


If the circumference of a circle measures 3/2TT cm, what is the area of the circle in terms of TT?
A. 3/4 tt cm2
B. 9/2 tt cm2
C. 9/4 tt cm2
D. 9/16 tt cm2

Answers

Answer:

A = pi 9/16  cm^2

Step-by-step explanation:

The circumference is 3/2 pi

The circumference is given by

C = 2 * pi *r

3/2 pi = 2 * pi *r

Divide each side by 2 *pi

3/2 pi / 2 pi  = 2 pi r /2pi

3/4 cm = r

Now we can find the area

A = pi r^2

A = pi ( 3/4) ^2

A = pi 9/16  cm^2

Answer:

d) 9/16π cm²

Step-by-step explanation:

Circumference = 3/2π cm

diameter = 3/2 cm

radius = 3/2 ÷ 2 = 3/4 cm

area = π(3/4)² = 9/16 π cm²

In 2020, you purchase a car for $8000. The value of the car depreciates by 4% each year. What will the approximate value of the car be in 2027? *

Answers

Answer:

Step-by-step explanation:

pls answer any that you can!!!

Answers

Answer:

12, 45, 1.8, -9, 18

Step-by-step explanation:

up up down down left right left right  b a start

Find the slope of the line that passes through (1, 11) and (9, 10).

Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Answers

Answer:

i think it would be negative. -1/8

help me plz with that ​

Answers

I’m really sorry but I can only narrow it down to economic and coercive. I’m leaning closer to coercive because it does seem more of a threat rather than a fact.

Select the statement that describes this expression: 8 + fraction 1 over 2 x (6 − 2) − 1. (2 points)

Group of answer choices

8 more than half the difference of 2 and 1, and then subtract 6

Add 8 to half the difference of 6 and 2, then subtract 1

The sum of 8 and fraction 1 over 2 times 6 plus 2 minus 1

1 less than half of 6 plus the sum of 8 and 2

Answers

Answer:

B

Step-by-step explanation:

Add 8 to half the difference of 6 and 2, then subtract 1. Therefore, the option B is the correct answer.

What is PEDMAS rule?

PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.

The given expression is 8+ 1/2×(6-2)-1

= 8+1/2×4-1

= 8+2-1

= 10-1

= 9

Therefore, the option B is the correct answer.

Learn more about the PEDMAS rule here:

https://brainly.com/question/24086845.

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what fraction is bigger? 7/10, 1/5, 9/10

Answers

The correct answer is 9/10

Mr. Kramer bought his daughter a kitten for her birthday, so now he needs to buy cat food. First, he gets a 20-pound bag of dry cat food. Then, he finds a good deal on 3-ounce cans of wet cat food, so he buys 48 of them. How many pounds of cat food does Mr. Kramer get in all?

Answers

Answer: 29 lbs

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The required pounds of cat food Mr. Kramer get in all is 9.

given that,

First, he gets a 20-pound bag of dry cat food.
Then, he finds a good deal on 3-ounce cans of wet cat food,
so he buys 48 of them.
It is to determine how many pounds of cat food Mr. Kramer get in all.

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements.

In a can, there are 3 ounces of wet cat food.
1 can = 3 ounce
multiplying both sides by 48
48 can = 3 * 48 ounce
48 can = 144 ounce
1 pound = 16 ounce
1/16 pound = 1 ounce
multiplying both sides by 144 on both sides
144 / 16 pound = 144 ounce
9 pound = 144 ounce

Thus, the required pounds of cat food Mr. Kramer gets in all is 9.

Learn more about arithmetic here:

brainly.com/question/14753192

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what is 1+1 please help me?

Answers

Answer:

2

Step-by-step explanation:

Answer:

Window :D

Step-by-step explanation:

Okay but it's 2 I gotchu bro

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Answers

Answer:

a. True, b. y = (-1/2)x + 8

Step-by-step explanation:

Because the graph is a straight line, that means that the graph is in fact proportional. For the equation, take the form y = mx+b. Plug in the slope, which is -1/2, and the y-intercept, which is 8, which would give you the equation y = (-1/2)x + 8.

Answer:

1) not proportional - not starting from origin

2) (2,8) - i did it in coordinates

have a great day

Which expression is equivalent to -1/3(6x + 15) - 3?

Answers

Answer:

6-x=0

Step-by-step explanation:

-2x+12=0(divide by 2)

6-x=0

Answer:

D is the answer
-2x-8

Step-by-step explanation:

I hope this helps! ^^

Cody's Seafood House purchases
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shrimp ?

Answers

Answer:

Try this

Step-by-step explanation:

So what you have to do is turn 65% into a decimal. 65% as a decimal is 0.65.

Then what you want to do is divide 5.00 and 0.65 and see what you get.

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Answers

It’s 54.77 it’s already rounded

The table below shows the different sizes of 15 pepperoni pizzas sold at a restaurant so far today.
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Answers

Answer:

2/3

Step-by-step explanation:

Find anequation of the line containing (3,-4) and having slope -2. If this line
contains the points (2,8) and (5.b), find a and b.​

Answers

Answer:

A linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we want to have a slope equal to -2, then our line will be something like:

y = -2*x + b

Now, we also want this line to pass through the point (3, -4)

This means that when x = 3, we must have y = -4

Then:

-4 = -2*(3) + b

-4 = -6 + b

-4 + 6 = b

2 = b

Then our line is:

y = -2*x + 2

Now, the second part says that:

If this line  contains the points (2,8) and (5.b), find a and b.​

This is incorrectly written because this line clearly does not contain the point (2, 8), so i guess the actual problem is something like:

If this line  contains the points (a,8) and (5.b), find a and b.​

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Answers

9514 1404 393

Answer:

8 white shirts22 colored shirts

Step-by-step explanation:

Let c represent the number of colored shirts sold. Then c-14 is the number of white shirts sold. The total revenue is ...

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22 colored shirts and 8 white shirts were sold.

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Answer:

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Tennis practice last for 1 hour and 35 minutes

Answers

Answer:

Where's the rest of this question??

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Answers

So out of the 2 pies there would be 16 pieces

Answer:

there is 16 pieces

Step-by-step explanation:

Four boys shared an apple. The amount each boy ate is listed below. Joey ate 1 2 of the apple. Max ate 1 8 of the apple. Chris ate 1 8 of the apple. Kevin ate 1 8 of the apple. How much of the apple did they eat altogether?

Answers

7/8

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I need help!
Can you help me please!

Answers

Answer:

Step-by-step explanation:

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Then, you simplify and add. you should get 23.0625=X^2

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Thirty eight years ago George was 14. how old is he now

Answers

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Answer:

I believe you need to add 38 and 14 together to get answer of 52 years old.

the length of a rectangle is 6 feet longer than its width the perimeter is less than 48 feet write a mathematical expression for the width of the rectangle

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Approximately 32800 citizens of a country died in automobile accidents in 2015

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Answer:

question is???

Step-by-step explanation:

Can someone help me? =)

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The letters A,B and C

please help me pleassee​

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it's a prism that is good question it's a prism ok a prism

Answer:

A prism.  A pyramid would look a little different, and flat too.

Hope that helps!

Step-by-step explanation:

Spaulding is the leading maker for basketballs in the US. Spaulding prides itself on the quality that its basketballs have the right amount of bounce when it is taken out of the packaging. They want their product to be ready for use upon opening. The air pressure of a particular ball has a target value of 7.9 PSI. Suppose the basketballs have a normal distribution with a standard deviation of 0.20 PSI. When a shipment of basketballs arrive, the consumer takes a sample of 21 from the shipment and measures their PSI to see if it meets the target value, and finds the mean to be 7.3 PSI. Perform this hypothesis test at the 5% significance level using the critical value approach.

Answers

Answer:

0 < 0.05, which means that we reject the null hypothesis, meaning that the air pressure of the balls is different of the target value of 7.9.

Step-by-step explanation:

The air pressure of a particular ball has a target value of 7.9 PSI.

This means that the null hypothesis is:

[tex]H_{0}: \mu = 7.9[/tex]

The alternate hypothesis is:

[tex]H_{a}: \mu \neq 7.9[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

The hypothesis tested means that [tex]\mu = 7.9[/tex]

Suppose the basketballs have a normal distribution with a standard deviation of 0.20 PSI.

This means that [tex]\sigma = 0.2[/tex]

When a shipment of basketballs arrive, the consumer takes a sample of 21 from the shipment and measures their PSI to see if it meets the target value, and finds the mean to be 7.3 PSI.

This means that [tex]X = 7.3, n = 21[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{7.3 - 7.9}{\frac{0.2}{\sqrt{21}}}[/tex]

[tex]z = -13.74[/tex]

pvalue:

We are testing that the mean pressure is different than the target value of 7.9, and since the test statistic is negative, the pvalue is 2 multiplied by the pvalue of z = -13.74, which we find looking at the z-table.

[tex]z = -13.74[/tex] has a pvalue of 0.

2*0 = 0

0 < 0.05, which means that we reject the null hypothesis, meaning that the air pressure of the balls is different of the target value of 7.9.

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