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If 1.5 per cent of items produced by a manufcaturing 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 per cent of items produced by a manufcaturing units are known t...
Probability of a Sample with No Defective Item

Given:

- 1.5% of items produced by a manufacturing unit are defective
- Sample size = 200 items

To find:

- Probability that a sample of 200 items would contain no defective item

Solution:

- Let's assume that the probability of an item being defective is p = 0.015
- The probability of an item not being defective is q = 1 - p = 0.985
- To find the probability of a sample of 200 items containing no defective item, we need to use the binomial distribution formula:

P(X = 0) = (n choose x) * p^x * q^(n-x)

Where,
- n = sample size = 200
- x = number of defective items = 0
- (n choose x) = Combination of n items taken x at a time = (200 choose 0) = 1
- p = probability of an item being defective = 0.015
- q = probability of an item not being defective = 0.985

Putting the values in the formula, we get:

P(X = 0) = (200 choose 0) * 0.015^0 * 0.985^200
P(X = 0) = 1 * 1 * 0.0526
P(X = 0) = 0.0526

Therefore, the probability that a sample of 200 items would contain no defective item is 0.0526 or 5.26%.

Answer:

The correct answer is option A) 0.05.
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If 1.5 per cent of items produced by a manufcaturing units are known to be defective, what is the probability that a sample of 200 items would contain no defective item?a)0.05b)0.15c)0.20d)0.22Correct answer is option 'A'. Can you explain this answer?
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