This exercise looks at how well the Poisson distribution approximates the binomial distribution. Assume that $\displaystyle {n}={389}$ and $\displaystyle {p}={0.003}$ for a binomial distribution.

Find the exact probability of one success in 389 trials.
(Report answer accurate to 6 decimal places.)
$\displaystyle {P}{\left({1}\right)}=$

Find the approximate probability of one success in (an interval spanning) 389 trials.
(Report answer accurate to 6 decimal places.)
$\displaystyle {P}{\left({1}\right)}=$

Find the relative difference between the two values.
Recall, the formula $\displaystyle \frac{{\text{approximation}-\text{actual}}}{{\text{actual}}}\cdot{100}\%$ (Report answer as a percent accurate to 4 decimal places; you need not type the “%” symbol.)
rel diff = %