What percent of 84 is 12? Round to the nearest whole number.

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

3

Zanzabum

A pergunta não está bem formatada. No entanto, pelo que parece óbvio

Responda:

3 horas

Explicação passo a passo:

Fração de hora gasta por sessão = 3/4 horas por sessão

Se o exercício for feito apenas aos domingos

Número de domingos por mês = 4

Portanto, número de sessões = 4

Fração de horas por sessão * Número de sessões

3/4 * 4 = 3 horas

Portanto, 3 horas são dedicadas ao exercício por mês

6 0

3 years ago

WHAT IS THE PRODUCT OF: 7.21 x 4.2<br> PLEASE--

lesantik [10]

<h3><u>QU</u><u>ESTION</u><u>:</u></h3>

WHAT IS THE PRODUCT OF: 7.21 x 4.2

PLEASE--

<h3>SOLUTION AND ANSWER:</h3>

$\: \: \: \: \sf7.2 \: 1 \\ \sf \times \: \: \: \: 4.2 \\ \: \: \sf \overline{1 \: 4 \: 4 \: 2} \\ \sf + \: 2 \: 8 \: 8 \: 4 \: 0 \: \: \: \: \: \\ \sf \overline{ \orange{3 \: 0.2 \: 8 \: 2}}$

THEREFORE, <em><u>30.282</u></em> IS THE PRODUCT

HOPE THIS HELP YOU! HAVE A NICE DAY!

~kimtaetae92~

NOTE: Kindly see this answer from brainly app if you are in web to see the displayed formats here.

7 0

2 years ago

A leather vest multiplied vero 0.63 by 1.8 point what is the correct product

labwork [276]

The answers of the product is 1.8 * 0.63 = 1.134

4 0

3 years ago

Bajo del Gualicho has an elevation of - 72 meters. Lago Enriquillo has an elevation of - 46 meters. Note

Harman [31]

Answer: Bajo del Gualicho has a higher elevation than Lago Enriquillo.

Step-by-step explanation:

Since in this case the "elevations" are negative because are under sea level, we can call it depth.

In this sense, we are given the "elevations" or depths of two places:

Bajo del Gualicho: -72 m

Lago Enriquillo: -46 m

Keeping in mind we are actually talking about the depth of this places, we can say Bajo del Gualicho is deeper than Lago Enriquillo, and this is best expressed with the following inequality:

$G>E$

Where $G$ represents Bajo del Gualicho and $E$ represents Lago Enriquillo.

4 0

3 years ago

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