Mathematics, 24.02.2020 19:03 hamada11617

Approximately 26% of all pipework failures in chemical plants are caused by operator error. What is the probability that out of the next 30 pipework failures, at least 14 are due to operator error

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Answer from: kierraivey

1.17% probability that out of the next 30 pipework failures, at least 14 are due to operator error.

Step-by-step explanation:

For each pipework failure in chemical plants, there are only two possible outcomes. EIther it is caused by operator error, or it is not. For each failure, the probability of it being caused by operator failure is independent from other failures. So we use the binomial probability distribution to solve this problem.

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.

Approximately 26% of all pipework failures in chemical plants are caused by operator error.

This means that p = 0.26

What is the probability that out of the next 30 pipework failures, at least 14 are due to operator error

This is $P(X \geq 14)$ when n = 30

Using a binomial probability calculator, we have that

$P(X \geq 14) = 0.0117$

1.17% probability that out of the next 30 pipework failures, at least 14 are due to operator error.

Answer from: Quest

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the (original price) is $420.

0.7x = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

Answer from: Quest

Hmmm i had this before , give me a sec

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Approximately 26% of all pipework failures in chemical plants are caused by operator error. What is...

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