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IrinaK [193]
3 years ago
6

Consider the following binomial experiment. A company owns 4 machines. The probability that on a given day any one machine will

break down is 0.53. What is the probability that at least 2 machines will break down on a given day?a) 0.6960b) 0.5398c) 0.8638d) 0.0225e) 0.5806
Mathematics
1 answer:
const2013 [10]3 years ago
7 0

Answer:

There is a 73.11% probability that at least 2 machines will break down on a given day.

Step-by-step explanation:

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

There are 4 machines, so n = 4.

The probability that on a given day any one machine will break down is 0.53. This means that p = 0.53.

What is the probability that at least 2 machines will break down on a given day?

P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 2) = C_{4,2}.(0.53)^{2}.(0.47)^{2} = 0.3723

P(X = 3) = C_{4,3}.(0.53)^{3}.(0.47)^{1} = 0.2799

P(X = 4) = C_{4,4}.(0.53)^{4}.(0.47)^{0} = 0.0789

So

P(X \geq 2) = P(X = 2) + P(X = 3) + P(X = 4) = 0.3723 + 0.2799 + 0.0789 = 0.7311

There is a 73.11% probability that at least 2 machines will break down on a given day.

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3 years ago
Expand and simplify 4(2x +7) – 3(x + 5)
Vikentia [17]

Answer:

4\left(2x+7\right)-3\left(x+5\right)=5x+13

Step-by-step explanation:

Given the expression

4\left(2x+7\right)-3\left(x+5\right)

<u>Expand and simplify the expression</u>

4\left(2x+7\right)-3\left(x+5\right)

Expand  4(2x + 7) = 8x + 28                  

4\left(2x+7\right)-3\left(x+5\right)=8x+28-3\left(x+5\right)

Expand  -3(x + 5) = -3x - 15

                                 =8x+28-3x-15

Group like terms

                                  =8x-3x+28-15

Add similar elements:  8x - 3x = 5x

                                   =5x+28-15

Simplify

                                    =5x+13

Therefore, we conclude that:

4\left(2x+7\right)-3\left(x+5\right)=5x+13

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2 years ago
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irina [24]

Answer:

Therefore the value of y(1)= 0.9152.

Step-by-step explanation:

According to the Euler's method

y(x+h)≈ y(x) + hy'(x) ....(1)

Given that y(0) =3 and step size (h) = 0.2.

y'(x)= x^2y(x)-\frac12y^2(x)

Putting the value of y'(x) in equation (1)

y(x+h)\approx y(x) +h(x^2y(x)-\frac12y^2(x))

Substituting x =0 and h= 0.2

y(0+0.2)\approx y(0)+0.2[0\times y(0)-\frac12 (y(0))^2]

\Rightarrow y(0.2)\approx 3+0.2[-\frac12 \times3]    [∵ y(0) =3 ]

\Rightarrow y(0.2)\approx 2.7

Substituting x =0.2 and h= 0.2

y(0.2+0.2)\approx y(0.2)+0.2[(0.2)^2\times y(0.2)-\frac12 (y(0.2))^2]

\Rightarrow y(0.4)\approx  2.7+0.2[(0.2)^2\times 2.7- \frac12(2.7)^2]

\Rightarrow y(0.4)\approx 1.9926

Substituting x =0.4 and h= 0.2

y(0.4+0.2)\approx y(0.4)+0.2[(0.4)^2\times y(0.4)-\frac12 (y(0.4))^2]

\Rightarrow y(0.6)\approx  1.9926+0.2[(0.4)^2\times 1.9926- \frac12(1.9926)^2]

\Rightarrow y(0.6)\approx 1.6593

Substituting x =0.6 and h= 0.2

y(0.6+0.2)\approx y(0.6)+0.2[(0.6)^2\times y(0.6)-\frac12 (y(0.6))^2]

\Rightarrow y(0.8)\approx  1.6593+0.2[(0.6)^2\times 1.6593- \frac12(1.6593)^2]

\Rightarrow y(0.6)\approx 0.8800

Substituting x =0.8 and h= 0.2

y(0.8+0.2)\approx y(0.8)+0.2[(0.8)^2\times y(0.8)-\frac12 (y(0.8))^2]

\Rightarrow y(1.0)\approx  0.8800+0.2[(0.8)^2\times 0.8800- \frac12(0.8800)^2]

\Rightarrow y(1.0)\approx 0.9152

Therefore the value of y(1)= 0.9152.

4 0
3 years ago
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