The Weibull distribution is widely used in statistical problems relating to aging of solid insulating materials subjected to aging and stress. Use this distribution as a model for time (in hours) to failure of solid insulating specimens subjected to AC voltage. The values of the parameters depend on the voltage and temperature; suppose α = 2.6 and β = 220. (a) What is the probability that a specimen's lifetime is at most 250? Less than 250? More than 300? (Round your answers to four decimal places.) at most 250 less than 250 more than 300 (b) What is the probability that a specimen's lifetime is between 100 and 250? (Round your answer to four decimal places.) (c) What value is such that exactly 50% of all specimens

Answers

Answer 1

Answer:

a

  P(X \le 250 ) =  0.7564 [/tex]  ,  [tex]P(X <  250 )  =  0.7564 [/tex]   ,

    [tex]P(X <  300 )  =  0.09922 [/tex]

b

[tex]P(100 <  X  < 250 ) =0.644 [/tex]

c

 [tex]   x  = 192.1   [/tex]

Step-by-step explanation:

From the question we are told that

   The value for [tex]\alpha  =  2.6[/tex]

    The value for [tex]\beta = 220[/tex]

Generally the  Weibull distribution function is mathematically represented as

      [tex]F( x , \alpha ,  \beta ) =  \left \{  0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \  x < 0} \atop { 1- e^{-(\frac{x}{\beta } )^{\alpha } }}\ \ \ \ \ \ x \ge 0} \right[/tex]

Generally the probability that a specimen's lifetime is at most 250 is mathematically represented as

      [tex]P(X \le  250 ) =  F(250, 2.7 , 220 )[/tex]

      [tex]P(X \le 250 )=1 - e^{- (\frac{250}{220} )^{2.7}}[/tex]

      [tex]P(X \le 250 ) =  1 - 0.2436[/tex]

      [tex]P(X \le 250 ) =  0.7564 [/tex]

Generally the probability that a specimen's lifetime is less than 250

      [tex]P(X <  250 ) =  F(250, 2.7 , 220 )[/tex]

      [texP(X <  250 ) =1 - e^{- (\frac{250}{220} )^{2.7}}[/tex]

      [tex]P(X <  250 )  =  1 - 0.2436[/tex]

      [tex]P(X <  250 )  =  0.7564 [/tex]    

Generally the probability that a specimen's lifetime is more than 300

     [tex]P(X >  300 ) = 1- p(X \le 300 )[/tex]

      [tex]P(X >  300 ) = 1-  F(300, 2.7 , 220 )[/tex]

      [texP(X <  300) =1- [1 - e^{- (\frac{300}{220} )^{2.7}}][/tex]

      [tex]P(X <  300 )  =  0.09922 [/tex]

Generally the probability that a specimen's lifetime is between 100 and 250 is

     [tex]P(100 <  X  < 250 ) =  P(X < 250) - P(X < 100)[/tex]

=>  [tex]P(100 <  X  < 250 ) =F(250 , 2.7 , 220 ) - F(100 , 2.7 , 220 ) [/tex]

=>  [tex]P(100 <  X  < 250 ) =(1 - e^{-(\frac{250}{220})^{2.7}}) - (1 - e^{-(\frac{100}{220})^{2.7}}) [/tex]

=>  [tex]P(100 <  X  < 250 ) = (1 - 0.244 ) - (1- 0.888)[/tex]

=>  [tex]P(100 <  X  < 250 ) =0.644 [/tex]

Generally the value  such that exactly 50% of all specimens

    [tex]P(X > x) = 1-P(X <  x) = 0.50[/tex]

=>  [tex]P(X > x) = 1- (1 - e^{- (\frac{x}{220}) ^{2.7}}) = 0.50[/tex]

=>  [tex] P(X> x ) = e^(- \frac{x}{20})^{2.7}  = 0.50 [/tex]

=>  [tex] P(X> x ) = (- \frac{x}{20})^{2.7}  = ln0.50 [/tex]

=>   [tex] P(X> x ) =  \frac{x}{20}  =[ -ln0.50 ] ^{frac{1}{2.7}}[/tex]

=>   [tex]   x  = 220[ -ln0.50 ] ^{frac{1}{2.7}}[/tex]

=>   [tex]   x  = 192.1   [/tex]

     


Related Questions

The distance from El Paso Texas to Houston

Texas is approximately 746 miles. If you

have already traveled 296 miles and you plan

on driving at a constant rate of 75 miles per

hour, how long will it take to get to Houston?

Answers

Answer:

It will take 6 hours to get to Houston.

Step-by-step explanation:

We have a total distance:

[tex] d_{T} = 746 mi [/tex]      

And, the distance traveled is:

[tex] d = 296 mi [/tex]

The plan is driving at a constant rate of 75 mi/h, so the time to get to Houston is:

[tex]t = \frac{x}{v}[/tex]

Where:

[tex] x = d_{T} - d = 746 mi - 296 mi = 450 mi [/tex]

[tex]t = \frac{x}{v} = \frac{450 mi}{75 mi/h} = 6 h[/tex]

Therefore, it will take 6 hours to get to Houston.

I hope it helps you!

Do these 3 side lengths form a right triangle? (Yes or no question): 10 cm, 49.5 cm, 50.5 cm

Answers

Answer:

yes

Step-by-step explanation:

By the converse of Pythagoras' identity.

If the longest side squared is equal to the sum of the squares of the other 2 sides, then the triangle is right.

longest side = 50.5

50.5² = 2550.25

10² + 49.5² = 100 + 2450.25 = 2550.25

Thus the given triangle is right.

Answer:

yes and no

Step-by-step explanation:

It is because there and different types of triangles and you were not specific with you question

2x + y = 12
- 3x + y = 2

Answers

the answer is y= -2/3x+4

6x - 2 - 3x = 16 steps ?

Answers

Answer:

i am very sure but i think this the answer

Step-by-step explanation:

 3x • (2x - 1)

[tex]\bold{Answer:}[/tex]x=6


[tex]\bold{Explanation:}[/tex]6x-2-3x=16
3x-2=16
3x=18
x=6

write your answer here

Answers

[tex]0.0063 = 63 \times {10}^{ - 4} = 6.3 \times {10}^{ - 3} \\ [/tex]

Done... ♥️♥️♥️♥️♥️

Answer:

what she said ^^ :)

Given a 30-60-90 triangle with a hypotenuse of 11 mm solve for the other sides. (Explain)

Answers

Answer:

Need a calculator

Step-by-step explanation:

This will be hard to explain without the ability to draw an example.

The one thing you can memorize is SOH - CAH - TOA

This stands for SIN(Opposite/Hypotenuse), COS(Adjacent/Hypotenuse) and TAN(Opposite/Adjacent).

When you know the angles of a right triangle and at least one side length, you can get the length of all the sides.

So a right triangle has two legs (sides) and the hypotenuse.  If you use the first angle ( 30 degrees)  you can use the formulas above to calculate the side length.

Pick either the SOH or the CAH.  Let's use SOH and write out the equation:

SIN(30 degrees) = Opposite Side divided by the Hypotenuse (11mm)

You can solve for the Opposite Side by multiplying both sides of the equal sign with 11mm.    You end up with SIN(30 degrees) X 11m = Opposite Side.

So the side directly across from the 30 degree angle should be 5.5mm

You can do the exact same thing with the 60 degree angle.

SIN(60 degrees) = Opposite Side divided by Hypotenuse (11mm)   OR

SIN(60 degrees) X 11mm = Opposite Side

This comes out to about 9.5mm

You can check the math by using the other equation CAH

Start with the 30 degree angle and solve for the adjacent side.  This is the side that is touching the 30 degree angle.  Equation will be

COS(30 degrees) X 11mm = Adjacent Side  or  about 9.5mm

The other equation will give you the side that is touching the 60 degree angle.

COS(60 degrees)  X 11mm = Adjacent Side or  5.5mm

You can also use one last thing to check your math.  The Pathagorean Theorem says in a right triangle  [tex]A^{2}[/tex] + [tex]B^{2}[/tex] = [tex]C^{2}[/tex] where C is the hypotenuse and A and B are the two sides.

[tex]5.5^{2}[/tex]  +  [tex]9.5^{2}[/tex]  should equal  [tex]11^{2}[/tex].  Give or take a few decimal places, it's almost exactly 11 (10.977 to be exact).

HEY answer this question so you can win. The answer has to be right or no winning 1000 dollors.

Answers

Answer: 21/3-5=2, -11/3+5 2/3=2

heres another im stuck on
im so bad at slopess

Answers

Answer:

1. e

2. d

3. b

4. c

Step-by-step explanation:

Hope This Helps!

Plz Mark Brainliest!

HURRY PLEASE!! I’ll mark you as brainliest
Tonya's class planted sunflowers and the students are tracking the growth of their individual plants. The table
shows the height of
Tonya's plant t days after she planted her sunflower seed

Based on the data in the table, what function h(t) represents the height, h, in inches, at time t?

Answers

Answer:

Here's what i did

Step-by-step explanation:

The answer is h = 0.4t

A linear function is a function in the form of:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

We can use the data in the table to find the relationship between the time (t) and height (h)

Let us use the format (height, time). Hence from the table, we have the points:

(4, 10), (8, 20), (12, 30) and (16,40). Using any two points, in this case (4, 10) and (16,40), we can apply the formula:

[tex]h-h_1=\frac{h_2-h_1}{t_2-t_1} (t-t_1)\\\\h-4=\frac{16-4}{40-10} (t-10)\\\\h-4=0.4(t-10)\\\\h-4=0.4t-4\\\\h = 0.4t[/tex]

Find out more at: https://brainly.com/question/13911928

HELP pleasee and ty to whoever does!!

Answers

Answers:
26) 50 percent chance
27) 25 percent chance
28) About 25 times
29) About 20 times

14. A cable company charges a $30 base installation fee plus $10 for every hour it takes to install all the equipment in your house. Write an equation in slope-intercept form that models the price of your installation as a function of the amount of time it takes.
A. y=30x+10
B. y=10x+30
C. y=10x-30
D. y=30x-10​

Answers

the answer is B
Y= $10( hours) + $30
So you multiply $10 (x) how many hours worked plus $30 charge for base . Will give you the (y)

Select the correct answer from each drop-down menu.

This image may be the result of the .
If m∠RQS is 75°, then m∠TPU is °. Select the correct answer from each drop-down menu.

Answers

Answer:

- construction of a line parallel to line AB through point P

∠TPU is 75°

Step-by-step explanation:

For Plato users

The image may be the result of the construction of a line parallel to line AB through point P

∠RQS is equal to ∠TPU;therefore, ∠TPU is also 75°

Answer:

below

Step-by-step explanation:

Got it right

school sold 2 adult tickets and 10 child tickets for a total of $56. The school took in $52 on the second
The school that Elisa goes to is selling tickets to a fall musical. On the first day of ticket sales the
second day by selling 4 adult tickets and 5 child tickets. What is the price each of one adult
ticket and one child ticket?

Answers

Answer:

x+y=4+8=12

$12 for one of each

or if you mean indivually (the wording confused me)

$4 for child, $8 for adult

Step-by-step explanation:

x=adult

y=child

2x+10y=56

4x+5y=52

iin order to be able to subtract values and find x and y im going to multiply 4x+5y=52 by two and get 8x+10y=104

8x+10y=104

-2x+10y=56

6x=48 divide each side by 6

x=8

plug 8 back into an equation to find cost of y

2(8)+10y=56

-16            -16

10y=40

y=4

I need helpppp IDKK

Answers

Answer:

Step-by-step explanation:

Choice

Answer:

Can you award me brainest

Which pair shows equivalent expressions? PLEASE HURRY IM BEING TIMED!!!!

Answers

Answer:

-2x-10=-2(x+5)

Step-by-step explanation:

Answer:

it's the third one

Step-by-step explanation:

I believe on doing homework to good luck with your work hope this helps

Write the vocabulary word for: A ratio of two quantities with different units.

We dont have vocab words in class so....

Answers

Answer:

a rate

Step-by-step explanation:

I looked it up :P

When finding the product, what is the first step?
(-c)x(-2a)x12b
btw the x's are multiply signs.
Thanks :)

Answers

Answer:

24abc

Step-by-step explanation:

(-c)*(-2a)*12b

Multiply the numbers

-1 * -2 *12 = 24

Multiply the variables

c*a*b = abc

Put it back together

24abc

12(4x -1/4x ) 2 + 5(4x-1/4x) - 2

solve it​

Answers

X= -28/17 =1.647
"1.5" was replaced by "(15/10)".

5*(4*x-(15/10)*x)+12-(4*x-2)=0

Simplify 3/2

3
((5 • (4x - (— • x))) + 12) - (4x - 2) = 0
2

Subtracting a fraction from a whole

Rewrite the whole as a fraction using 2 as the denominator :

Adding a whole to a fraction

Rewrite the whole as a fraction using 2 as the denominator

Subtracting a whole from a fraction

Rewrite the whole as a fraction using 2 as the denominator

Pull out like factors :

4x - 2 = 2 • (2x - 1)

When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

17x+28
—————— • 2 = 0 • 2
2
Now, on the left hand side, the 2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
17x+28 = 0

Solve the equation: 5.1 - 7x = 9.1

Answers

Answer:

Order summands

2

Subtract

5

.

1

5.1

5.1

from both sides of the equation

3

Simplify

4

Divide both sides of the equation by the same term

5

Simplify

Step-by-step explanation:

Create a one step equation using the numbers 4 and 6. One you create the
equation, solve it and find the solution.

Answers

Answer:

x=1.5

Step-by-step explanation:

4x=6

6/4=1.5

. What is the 11th term of the geometric sequence {1,000,000; 100,000; 10,000; …}?

Answers

A shortcut to doing this is to use exponential notation. 1,000,000 = 10^6...10^(6-11)...10^-5= 0.00001
0.0001

it decreases by dividing 10 each time so your answer will be 0.0001

Simplify 2x+3y^2-2(x-Y)

y^2, 2y^2, 4y^2, or 5y^2​

Answers

Answer:

3y^2+2y

Step-by-step explanation:

A beef stew recipe calls for 3 cups of vegetable juice. Find the number of fluid ounces of vegetable juice needed for the recipe.

Answers

Answer:

24 fluid ounces

Step-by-step explanation:

24 fluid ounces because 8 fluid ounces is 1 cup

Please help me Evaluate -9 - (-4)

Answers

Answer:

Should be 13. Sorry if I’m incorrect!

Step-by-step explanation:

the answer is -5 because the minus after the 9 and the -4 in the parentheses makes the minuses a adding sign

If the perimeter of the regular pentagon is 75 cm what is the length of each side

Plz help nowww

If you wanna be crowed a brainliest:-)

Answers

Answer:

15 (mark me brainliest if you want and lmk if you need more help understanding)

Step-by-step explanation:

perimeter is (l*w)*2

if a pentagon is 5 sided, you do 75/5 which is 15.

each side has 15 cm

PLEASE HELP ASAP! (picture is attached) You real one if you do

Answers

Answer:

x is equal to 1

Step-by-step explanation:


What is the pattern as the exponents decrease?

Answers

Can we see the patern please

Which best explains the relationship between the two triangles below? Triangle D C A. Angle D is 51.2 degrees and angle A is 96.5 degrees. Triangle S R T. Angle S is 32.3 degrees and angle R is 96.5 degrees. Triangle A D C is similar to triangle R T S because Angle A is congruent to angle R, Angle C is congruent to angle S, and Angle D is congruent to angle T. Triangle A D C is similar to triangle R T S because Angle A is similar to angle R, Angle C is similar to angle S, and Angle D is similar to angle T. Triangle A D C is not similar to Triangle R T S because Angle D is not congruent to Angle S. Triangle A D C is not similar to Triangle R T S because C D less than S T, D A less than T R, and C A less than S R.

Answers

Answer:

Answer is A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

i just take the test

what is the next 3 terms for (-6,42,-294,2058)

Answers

Answer:

es

Step-by-step explanation:

Answer:

A. 14,406. it runs by a -7 sequence, so D would be the 6th in the sequence.

Step-by-step explanation:

The volume of a cylinder is given by the formula y = rrah, where r is the radius of the cylinder and h is the height.
Which expression represents the volume of this cylinder?
n = 2x + 7
0 0
0 24x3 – 12xx2 - 24 xX+63%
O 28x3 - 5 xX2 – 24 xX+63x
O 28x3 + 7 xx? - 18xx-63

Answers

The third one is the correct answer I think

The volume of the cylinder with radius r = x - 3 and height h = 2x + 7 is given by the expression V = π ( 2x³ - 5x² - 24x + 63 )

What is a Cylinder?

A cylinder is a three-dimensional shape consisting of two parallel circular bases, joined by a curved surface. The center of the circular bases overlaps each other to form a right cylinder. The volume of a cylinder is

Volume of Cylinder = πr²h

Surface area of cylinder = 2πr ( r + h )

where r is the radius of the cylinder

h is the height of the cylinder

Given data ,

Let the volume of the cylinder be represented as V

Now , the radius of the cylinder r = ( x - 3 ) units

Let the height of the cylinder be h = ( 2x + 7 ) units

And , Volume of Cylinder = πr²h

On simplifying the equation , we get

Volume of Cylinder = π ( x - 3 )² ( 2x + 7 )

Volume of Cylinder = π ( x² - 6x + 9 ) ( 2x + 7 )

On further simplification , we get

Volume of Cylinder = π ( 2x³ - 5x² - 24x + 63 )

Hence , the expression for the cylinder is V = π ( 2x³ - 5x² - 24x + 63 )

To learn more about cylinder click :

https://brainly.com/question/16134180

#SPJ7

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