Business, 24.07.2019 16:10, cici86

Aquality control inspector has drawn a sample of 18 light bulbs from a recent production lot. if the number of defective bulbs is 2 or more, the lot fails inspection. suppose 30% of the bulbs in the lot are defective. what is the probability that the lot will fail inspection? round your answer to four decimal places.

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answered: alex43079

0.9858

Explanation:

Binomial distribution formula

$P(X=x)=^nC_x\ p^x\ (1-p)^{n-x}$ , where P(x) is the probability of getting success in x trials , n is total number of trials and p is the probability of getting success in each trial.

Given : The probability that bulbs in the lot is defective = 0.30

Sample size = 18

If the number of defective bulbs is 2 or more, the lot fails inspection.

Then , the probability that the lot will fail inspection is given by :-

$P(X\geq2)=1-(P(X$

Hence, the probability that the lot will fail inspection =0.9858

answered: krrrr

There is a 98.58% probability that the lot will fail inspection.

Explanation:

For each light bulb in the production lot, there are two possible outcomes. Either they are defective, or they are not. This means that we can solve this problem using concepts of the binomial probability 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 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 18 light bulbs, so n = 18 .

30% of the bulbs in the lot are defective. This means that p = 0.3 .

If the number of defective bulbs is 2 or more, the lot fails inspection. Suppose 30% of the bulbs in the lot are defective. What is the probability that the lot will fail inspection?

This is $P(X \geq 2)$ .

Either there are 2 or more defective bulbs, or there are less than two. The sum of the probabilities of these events is decimal 1. So:

$P(X < 2) + P(X \geq 2) = 1$

$P(X \geq 2) = 1 - P(X < 2)$

In which

P(X < 2) = P(X = 0) + P(X = 1)

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

$P(X = 0) = C_{18,0}.(0.30)^{0}.(0.70)^{18} = 0.0016$

$P(X = 1) = C_{18,1}.(0.30)^{1}.(0.70)^{1t} = 0.0126$

P(X < 2) = P(X = 0) + P(X = 1) = 0.0016 + 0.0126 = 0.0142

Finally

$P(X \geq 2) = 1 - P(X < 2) = 1 - 0.0142 = 0.9858$

There is a 98.58% probability that the lot will fail inspection.

answered: Guest

What do you mean by that?

answered: Guest

it's actually a very difficult task, due to not many people can make 2 million dollars in 2 years. besides that, to the not-so-realistic ideas, you can create a business. it could be practically anything, but make it into a business that isn't that known yet, you get me? also, lets not forget about stock market. that's where all the good stuff happens. use investments at the beginning and begin to raise up your business or whatever you're going to do. as this is a very non-realistic idea, it's still worth the shot!

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Aquality control inspector has drawn a sample of 18 light bulbs from a recent production lot. if the...