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f) The life of a power transmission tower is exponentially distributed, with mean life 25 years. If three towers, operated indep

Step2247 [10]

Answer:

15.24% probability that at least 2 will still stand after 35 years

Step-by-step explanation:

To solve this question, we need to understand the binomial distribution and the exponential distribution.

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 combinations 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.

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \mu e^{-\mu x}$

In which $\mu = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

Probability of a single tower being standing after 35 years:

Single tower, so exponential.

Mean of 25 years, so $m = 25, \mu = \frac{1}{25} = 0.04$

We have to find $P(X > 35)$

$P(X > 35) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-0.04*35} = 0.2466$

What is the probability that at least 2 will still stand after 35 years?

Now binomial.

Each tower has a 0.2466 probability of being standing after 35 years, so $p = 0.2466$

3 towers, so $n = 3$

We have to find:

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

In which

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

$P(X = 2) = C_{3,2}.(0.2466)^{2}.(0.7534)^{1} = 0.1374$

$P(X = 3) = C_{3,3}.(0.2466)^{3}.(0.7534)^{0} = 0.0150$

$P(X \geq 2) = P(X = 2) + P(X = 3) = 0.1374 + 0.0150 = 0.1524$

15.24% probability that at least 2 will still stand after 35 years

4 0

3 years ago

What is -7 + -9 A. -16 B. -2 C. 2 D. 16

nataly862011 [7]

Answer:

is A. -16

Step-by-step explanation:

3 0

2 years ago

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PLEASE HELP ME, ILL BRAINLIEST YOU ill give u 30 points if you help

lisov135 [29]

Answer:

$x = 58$

$y = 90$

Step-by-step explanation:

This is a rhombus becuase it a quadralterial and it has four right triangles, and it diagonals bisect each others so it cant be a trapezoid, and paralleolgram. and it doesnt have four right corner angles so it cant be a square or rectangle or kite.

A rhombus inner angle measure is 90 degrees.

So

$y = 90$

This means the upper left angle of the top triangle measure is 58 becuase triangle interior theorem.

Since a rhombus bisects angles, angle x measure 58.

7 0

3 years ago

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(30 POINTS) The 20% off sale is a better deal than the $200 rebate or $150 coupon for the $1,500 dining set. The Porters budgete

Ratling [72]

<span>Yes, the Porters are under budget. The 20% off sale is the best deal because $1,500 times 0.20 is $300. $300 is a bigger discount than the $150 coupon and $200 rebate. $300 off $1,500 is $1,200, which is less than the amount budgeted.</span>

4 0

2 years ago

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What is the inverse of the function f(x) = x +3?

harkovskaia [24]

Answer:

x=y+3

Step-by-step explanation:

you just swap variables.

4 0

3 years ago