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CA Foundation · Quantitative Aptitude · Theoretical Distributions

A Chennai call-centre agent converts each call into a sale with probability 0.2, independently. If the agent makes 50 calls, what are the mean and standard deviation of the number of sales?

The mean is np = 50 × 0.2 = 10 sales. The variance is npq = 50 × 0.2 × 0.8 = 8, so the standard deviation is the square root of 8, about 2.83. Quoting 8 as the SD confuses variance with SD.

  1. AMean 10, standard deviation 2.83Correct
  2. BMean 10, standard deviation 8
  3. CMean 40, standard deviation 2.83
  4. DMean 10, standard deviation 3.16

Explanation

Mean = np = 50 × 0.2 = 10. Variance = npq = 50 × 0.2 × 0.8 = 8, so SD = √8 ≈ 2.83. Option with SD 8 gives the variance rather than the SD; SD 3.16 is √10, i.e. the square root of the mean.

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