Equivalent equation for 3p+12m+8

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

2 years ago

Hans bought 3 CDs that were each the same price. Including sales tax, he paid a total of 41.10. Of that total, 2.40 was tax. Wha

Olin [163]

Answer:

Each CD cost 12.90 before tax

Step-by-step explanation:

41.10-2.40=38.7

38.7/3=12.90

4 0

2 years ago

A long distance phone service charges $0.30 for the first 10 minutes and $0.05 for each additional minute or fraction thereof. U

olga nikolaevna [1]

Answer: Our Cost function is discontinuous at every integer after x>10.

Step-by-step explanation:

Since we have given that

For the first 10 minutes , the service charges = $0.30

Let the number of additional minute be 't'.

Amount charge for each additional minute = $0.05

Using the greatest integer function:

So, Cost C of a call in terms of time 't' minutes would be

$C=0.03+0.05\left \lceil t-10 \right \rceil$

As we know that Greatest integer is discontinuous at every integer.

So, our Cost function is discontinuous at every integer after x>10.

4 0

3 years ago

Website A gets 5,000,000 hits in one day. Website B gets 4,000 hits in one day. Approximately how many times more hits does Webs

ArbitrLikvidat [17]

Answer:

<u>1,250</u> times more hits does Website A get than Website B.

Step-by-step explanation:

Given:

Website A gets 5,000,000 hits in one day.

Website B gets 4,000 hits in one day.

Now, to find the times more hits Website A get than Website B.

Website A gets hits in one day = 5,000,000.

Website B gets hits in one day = 4,000.

So, to get the number of times more Website A get than Website B we divide Website A gets hits in one day by Website B gets hits in one day:

$5,000,000\div 4,000$

$=1,250.$

Therefore, 1,250 times more hits does Website A get than Website B.

5 0

2 years ago

Julie and Tom each earn money at thier part time job.

Fudgin [204]

And then they bought food

5 0

3 years ago