g The average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. A lot contains 200 of these vehicles, brand new. What is the probability that 50 or more of them fail in the first 2 years

Answers

Answer 1

Answer:

The probability is [tex]P(A \ge 50 ) = 0.14321[/tex]

Step-by-step explanation:

The average life span is  [tex]\pi = 8[/tex]

The sample size is n =  200

Generally we are told that average lifespan for a certain type of vehicle follows an exponential distribution

i.e  

             [tex]X \~ \ \ \ exp(8)[/tex]

Gnerally the probability distribution function for exponential distribution is

       [tex]f(x) = \left \{ {{\lambda * e^{-\lambda * x }\ \ \ x\ge 0 } \atop {0 \ \ \ \ \ \ \ \ \ \ x < 0}} \right.[/tex]

Now [tex]\lambda[/tex] is the  constant which is evaluated as

      [tex]\lambda = \frac{1}{\pi}[/tex]

=>   [tex]\lambda = \frac{1}{8}[/tex]

=>   [tex]\lambda = 0.125[/tex]

Generally the that the vehicles will fail in less than 2 years is  mathematically represented as

         [tex]P(X \le 2 )= p= \int\limits^2_0 {\lambda e^{- \lambda * x} } \, dx[/tex]

        [tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * x} } ]|\left 2 } \atop {0}} \right.[/tex]

       [tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 2} } ] - [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 0} } ][/tex]

     [tex]P(X \le 2 )= p= -0.77880 + 1[/tex]

     [tex]P(X \le 2 )= p= 0.2212[/tex]

Generally the probability that the vehicle will fail in the first 2 years follows a binomial  distribution  with the mean evaluated as

         [tex]\mu = n * p[/tex]

=>      [tex]\mu = 200 * 0.2212[/tex]

=>      [tex]\mu = 44.24[/tex]

The standard deviation is

       [tex]\sigma = \sqrt{np(1 - p)}[/tex]    

      [tex]\sigma = \sqrt{200 * 0.2212 (1 - 0.2212)}[/tex]  

      [tex]\sigma = 5.86[/tex]

Using normal approximation of binomial  distribution the  probability that 50 or more of them fail in the first 2 years is mathematically represented as

   [tex]P(A \ge 50 ) = 1 - P(A < 50 )[/tex]

Applying continuity correction

    [tex]P(A \ge 50.5 ) = 1 - P(A < 50.5 )[/tex]

Here

    [tex]P(A < 50.5 ) = P(\frac{A - \mu }{\sigma} < \frac{50 - 44.24}{5.87} )[/tex]

Generally  

       [tex]\frac{A - \mu }{\sigma} = Z (The \ standardized \ value \ of A )[/tex]

=> [tex]P(A < 50.5 ) = P( Z < 1.0664 )[/tex]

From the z-table the probability value  of  ( Z  <  1.0664   ) is  

     [tex]P( Z < 1.0664 ) = 0.85679[/tex]

So  

   [tex]P(A \ge 50 ) = 1 - 0.85679[/tex]

=> [tex]P(A \ge 50 ) = 0.14321[/tex]


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Step-by-step explanation:

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DBYes

Step-by-step explanation:

x: cupcakes

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9514 1404 393

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  1.  d. 4x +32y ≤ 224

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Step-by-step explanation:

1. For x number of cupcakes, at 4 minutes each, the time required for their decoration is 4x.

For y number of cakes, at 32 minutes each, the time required for their decoration is 32y.

The total decorating time must be less than or equal to 224 minutes:

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__

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__

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Step-by-step explanation:

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Step-by-step explanation:

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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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Step-by-step explanation:

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Answers

Answer:   c

Step-by-step explanation:

Based on the percent breakdown of 360%.

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c

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answer:

4.84

Step-by-step explanation:

4.84 is the nearest hundredth number of 4.8367.

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Four point eight three six seven is the given decimal number.

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In the given decimal number the value at hundredth position is 3.

We need to follow the rules when rounding a decimal number.

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if it's 5 or more than you should round the previous digit up.

In the given decimal number on right of 3 it is 6 which is more than 5. So we need to round the increase the value of 3 by 1 which makes it 4.

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Answer:

4 - 2 = 2

Step-by-step explanation

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Answers

Answer: 6 kids walked to school

Step-by-step explanation:

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3.5
=
12
x
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Answers

Answer:

Sarah multiplied the denominator by the denominator and the numerator by the numerator instead of finding the cross products. The equation should be 5x = 42, so the cost should be $8.40.

Step-by-step explanation:

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Answers


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If we substitute all the x’s with 3, then we end up with 23 if we add all the sides.

(This means your original answer, 3 , is correct.)

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Answers

Answer:

(1, 6), (2, 8), (3, 10)

2(1) + 4 = 6, 2(2) + 4 = 8 and 2(3) + 4 = 10.

Step-by-step explanation:

The set of inputs for the equation f ( x ) = 2x + 4 is

( 1 , 6 ) , ( 2 , 8 ) , ( 3 , 10 )

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be f ( x ) = 2x + 4

f ( x ) = y

Now ,

Let the first point be A ( 1 , 6 )

Let the second point be B ( 2 , 8 )

Let the third point be C ( 3 , 10 )

a)

A ( 1 , 6 )

Substitute the value of x and y in the equation , we get

y = 2x + 4

6 = 2 ( 1 ) + 4

6 = 2 + 4

6 = 6

Hence , the input A ( 1 , 6 ) satisfies

b)

B ( 2 , 8 )

Substitute the value of x and y in the equation , we get

y = 2x + 4

8 = 2 ( 2 ) + 4

8 = 4 + 4

8 = 8

Hence , the input B ( 2 , 8 ) satisfies

c)

C ( 3 , 10 )

Substitute the value of x and y in the equation , we get

y = 2x + 4

10 = 2 ( 3 ) + 4

10 = 6 + 4

10 = 10

Hence , the input C ( 3 , 10 ) satisfies

Hence , The set of inputs for the equation f ( x ) = 2x + 4 is

( 1 , 6 ) , ( 2 , 8 ) , ( 3 , 10 )

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When are `x+2` and `3x` equal?
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Answers

Answer:

but tbh this equation cannot be equal

Step-by-step explanation:

Answer:

No, they are not equal, because you can not add x to 2, because it does not have an x after the 2, so they are not the same

Step-by-step explanation:

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