uppose you start at the origin, move along the x-axis a distance of 7 units in the positive direction, and then move downward al
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Using the binomial distribution, it is found that:
- 0.9599 = 95.99% probability that the company will find 2 or fewer defective products in this batch.
- 0.0066 = 0.66% probability that 4 or more defective products are found in this batch.
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For each product, there are only two possible outcomes, either it is defective, or it is not. The probability of a product being defective is independent of any other product, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the<u> probability of exactly x successes on n repeated trials.</u>
is the number of different combinations of x objects from a set of n elements, given by:
And p is the probability of a success on a single trial.
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- 24 products means that
- 3.2% are defective, thus
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The probability that <u>2 or fewer are defective</u> is:
In which
Thus
0.9599 = 95.99% probability that the company will find 2 or fewer defective products in this batch.
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The probability that <u>4 or more are defective</u> is:
In which
Then
Thus
0.0066 = 0.66% probability that 4 or more defective products are found in this batch.
A similar problem is given at brainly.com/question/23780714