Question

Let x be a binomial random variable with

n = 20

and

p = 0.05.

Calculate

p(0)

and

p(1)

using Table 1 to obtain the exact binomial probability. (Round your answers to three decimal places.)

p(0)

=

p(1)

=

Calculate

p(0)

and

p(1)

using the Poisson approximation. (Round your answer to three decimal places.)

p(0)

=

p(1)

=

Compare your results. Is the approximation accurate?

No the approximation is not accurate. At least one the differences between the probabilities from the Poisson approximation and the exact probabilities from the binomial distribution is much greater than 0.05.Yes the approximation is reasonably accurate. In general, the probabilities from the Poisson approximation are all well within 0.05 of the exact probabilities from the binomial distribution.     

You may need to use the appropriate appendix table or technology to answer this question.

Answer 1