CA Foundation · Quantitative Aptitude · Theoretical Distributions
Defects in a roll of cloth made in Ludhiana follow a Poisson distribution at 0.5 defects per metre. What is the mean number of defects in a 6-metre piece, and the standard deviation?
The mean is 3 defects and the standard deviation is about 1.732. The rate scales to 0.5 × 6 = 3 for the piece, and since a Poisson variance equals its mean, the standard deviation is the square root of 3.
- A3 and 3
- B3 and 1.732Correct
- C3 and 1.5
- D6 and 2.449
Explanation
Mean for 6 metres = 0.5 * 6 = 3. For a Poisson distribution variance = mean = 3, so the standard deviation is √3 = 1.732. Standard deviation 3 confuses it with the variance, and 1.5 wrongly takes half the mean.
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