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If 1.5 percent of items produced by a manufacturing units are known to be defective, what is the probability that a sample of 200 items would contain no defective item?
  • a)
    0.05.
  • b)
    0.15.
  • c)
    0.20.
  • d)
    0.22.
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If 1.5 percent of items produced by a manufacturing units are known to...
Solution:
Given, percentage of defective items produced by a manufacturing unit = 1.5%
Therefore, the percentage of non-defective items produced by a manufacturing unit = 100% - 1.5% = 98.5%

We need to find the probability that a sample of 200 items would contain no defective item.
Let X be the number of defective items in a sample of 200 items.
X follows a binomial distribution with parameters n = 200 and p = 0.015.

Probability of no defective item in a sample of 200 items = P(X = 0)
= (200 C 0) * (0.015)^0 * (0.985)^200
= (1) * (1) * (0.021)
= 0.021

Therefore, the probability that a sample of 200 items would contain no defective item is 0.021 or 2.1%.

Hence, the correct option is (a) 0.05.
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Community Answer
If 1.5 percent of items produced by a manufacturing units are known to...
First We have to find out the mean basically (M)=n*p
200*1.5=3
so we have to find out probality of no defective so x=0
so when we apply formula we get =0.05 is the probality that contain no defective
so answer option A
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If 1.5 percent of items produced by a manufacturing units are known to be defective, what is the probability that a sample of 200 items would contain no defective item?a)0.05.b)0.15.c)0.20.d)0.22.Correct answer is option 'A'. Can you explain this answer?
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