1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Marta_Voda [28]
2 years ago
11

4. Dean Pelton wants to perform calculations to impress the accreditation consultants, but upon asking for information about GPA

s at Greendale Community College, Chang only tells Pelton that the GPAs are distributed with a probability density function f(x) = D(2 + e −x ), 2 ≤ x ≤ 4 where D was some unknown "Duncan" constant. How many student records have to be retrieved so that the probability that the average GPA is less than 2.3 is less than 4 percent?
Mathematics
1 answer:
Leya [2.2K]2 years ago
5 0

Answer:

the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Step-by-step explanation:

Let assume that n should represent the number of the students

SO, \bar x can now be the sample mean of number of students  in GPA's

To obtain n such that P( \bar x \leq 2.3 ) \leq .04

⇒ P( \bar x \geq 2.3 ) \geq .96

However ;

E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D  \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D

E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D

Similarly;

D\int\limits^4_2(2+ e^{-x}) dx = 1

⇒ D*(2x-e^{-x} ) |^4_2 = 1

⇒ D*4.117 = 1

⇒ D= \dfrac{1}{4.117}

\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103

∴  Var (x)  = E(x^2) - E^2(x) \\ \\  = .3348711

Now; P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega  \geq .691013)  \ \ \ \  \ \ \ \ \ \ (x = E(\bar x ) - \mu)

Using Chebysher one sided inequality ; we have:

P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}

So; (\omega = \bar x - \mu)

⇒ E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}

∴ P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}

To determine n; such that ;

\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}

⇒ n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}

n \geq 16.83125

Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

You might be interested in
Choose the congruence theorem that you would use to prove the triangles congruent.
Elena L [17]

<u><em>Answer:</em></u>

SAS

<u><em>Explanation:</em></u>

<u>Before solving the problem, let's define each of the given theorems:</u>

<u>1- SSS (side-side-side):</u> This theorem is valid when the three sides of the first triangle are congruent to the corresponding three sides in the second triangle

<u>2- SAS (side-angle-side):</u> This theorem is valid when two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle

<u>3- ASA (angle-side-angle):</u> This theorem is valid when two angles and the included side between them in the first triangle are congruent to the corresponding two angles and the included side between them in the second triangle

<u>4- AAS (angle-angle-side):</u> This theorem is valid when two angles and a side that is not included between them in the first triangle are congruent to the corresponding two angles and a side that is not included between them in the second triangle

<u>Now, let's check the given triangles:</u>

We can note that the two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle

This means that the two triangles are congruent by <u>SAS</u> theorem

Hope this helps :)

5 0
3 years ago
Read 2 more answers
Which graph represents the solution set of this inequality?
lesya692 [45]

Answer:

the answer is C

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Need help thanks please :)
Nadya [2.5K]

Answer:

t:

\infty , -  \infty

meaning any number can substitute t and it would be the same answer.

7 0
3 years ago
Pam and Amanda and Mike work at different clothing stores. Amanda made twice what Pam earned and Julie
Dmitriy789 [7]

Answer:

Pam: $181

Amanda: $362

Julie: $452

Step-by-step explanation:

(What does Mike have to do with this problem?)

Let a = Amanda's pay

Let p = Pam's pay

Let j = Julie's pay

"Amanda made twice what Pam earned"

a = 2p

"Julie made $90 more than Amanda"

j = a + 90

j = 2p + 90

Pam earned p

Total salary

a + p + j = 2p + p + 2p + 90

Total salary

$995

2p + p + 2p + 90 = 995

5p = 905

p = 181

a = 2p = 2(181) = 362

j = 2p + 90 = 362 + 90 = 452

Answer:

Pam: $181

Amanda: $362

Julie: $452

8 0
3 years ago
Solve for the unknown values.<br> 95<br> х<br> 50<br> у<br> degrees<br> y =<br> degrees
vaieri [72.5K]

Answer:

One interior angle is 50°.

Exterior angle is 95°.

Step-by-step explanation:

6 0
2 years ago
Other questions:
  • The solutions to a certain quadratic equation are x = 4 and x = -3. Write the equation in standard form below.
    14·1 answer
  • If two angles are supplementary and one angle measures 47°, what is the measure of the other angle?
    6·2 answers
  • 1. Find six rational numbers between
    5·1 answer
  • Factor 6y + 8y 6y² +8y?​
    12·1 answer
  • 9. John bought a used truck for $4,500. He made an agreement with the dealer to put $1,500 down and make payments of $350 for th
    7·1 answer
  • PPPPPLLLLLLZZZZZZZ HEEEELLP
    5·1 answer
  • Use always, sometimes or never to make a true statement:
    5·1 answer
  • I think this is easy for yall but nor for me lol need help
    13·1 answer
  • Desperate Please Hurry Up
    10·1 answer
  • A bicycle is traveling at 12 miles per hour. How many feet will it cover in 30 seconds?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!