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CA Foundation · Quantitative Aptitude · Theoretical Distributions

Which of the following statements about the binomial, Poisson and normal distributions is correct?

The correct statement is that the normal distribution is symmetric with mean, median and mode equal. The others are false: Poisson variance equals its mean, binomial variance npq is below its mean np, and the normal is continuous with zero skewness.

  1. AThe Poisson distribution has variance always less than its mean
  2. BThe binomial distribution has mean always less than its variance
  3. CThe normal distribution is symmetric, with mean, median and mode equalCorrect
  4. DThe normal distribution is a discrete distribution with skewness greater than zero

Explanation

The normal curve is symmetric and bell-shaped, so mean, median and mode coincide. The Poisson has variance equal to its mean. The binomial has variance npq, which is less than the mean np. The normal is continuous, with zero skewness.

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