jweldene12
23.07.2021 •
Mathematics
it is found that 4% of watches produced at a particular factory are defective. If 20 watches made at this factory are randomly selected, what is the probbility that at mpst 1 watch in the same sample is found to be defective
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Ответ:
0.81 = 81% probability that at most 1 watch in the sample is defective.
Step-by-step explanation:
For each watch, there are only two possible outcomes. Either it is defective, or it is not. The probability of a watch being defective is independent of any other watch, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
4% of watches produced at a particular factory are defective.
This means that
20 watches made at this factory are randomly selected
This means that
What is the probability that at most 1 watch in the same sample is found to be defective?
This is:
In which
Then
0.81 = 81% probability that at most 1 watch in the sample is defective.
Ответ:
EXPLANATION
The given equation is
If we let
then, the equation becomes,
We split the middle term to get,
We now factor to obtain;
We factor further to obtain;
This implies that;
Or
Or
But we know that
This means that,
.
Or
Therefore