Questions and Answers
Which distribution can be approximated with normal distribution if the mean and standard deviation are sufficiently large and the distribution is symmetric?
Poisson distribution
Which of the following statements is true about the Poisson distribution?
It can only be approximated with normal distribution if mean and standard deviation are both large
Which distribution can be used to approximate probabilities of rare events and is simpler to work with mathematically?
Poisson distribution
What is the formula to transform a Poisson variable into a standard normal variable?
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Which formula is used to transform Poisson variable into standard normal variable?
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When can the Poisson distribution be used to approximate the binomial distribution?
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Study Notes
- Poisson distribution can be approximated with normal distribution if mean and standard deviation are sufficiently large, and distribution is symmetric.
- Normal distribution is easier to work with mathematically and is used in many statistical tests.
- Formula to transform Poisson variable into standard normal variable is Z = (X - μ) / σ.
- Binomial distribution can be approximated with Poisson distribution if number of trials is large and probability of success is small.
- Poisson distribution is simpler to work with mathematically and can be used to approximate probabilities of rare events.
- Formula to find Poisson parameter λ is λ = n * p.
- Probability mass function of Poisson distribution can be used to calculate probabilities of binomial distribution.
- Approximation is usually better for larger values of n and smaller values of p.
- Poisson approximation may not be accurate if n is small or p is large.
- Approximation is useful in situations where exact calculation of probabilities is difficult or time-consuming.
