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]

     


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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation:

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Answers

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Answers

Answer:

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2

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1

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Answers

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Answers

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Answers

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Answers

Answer:

yes

Step-by-step explanation:

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yes and no

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Answers

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

Step-by-step explanation:

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Answers

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Answers

the answer is B
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school sold 2 adult tickets and 10 child tickets for a total of $56. The school took in $52 on the second
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Answers

Answer:

x+y=4+8=12

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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.

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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).

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°

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below

Step-by-step explanation:

Got it right

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Answers

Answer:

Step-by-step explanation:

Choice

Answer:

Can you award me brainest

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