This exercise looks at how well the Poisson distribution approximates the binomial distribution. Assume that n=375\displaystyle {n}={375} and p=0.001\displaystyle {p}={0.001} for a binomial distribution.

Find the exact probability of one success in 375 trials.
(Report answer accurate to 6 decimal places.)
P(1)=\displaystyle {P}{\left({1}\right)}=

Find the approximate probability of one success in (an interval spanning) 375 trials.
(Report answer accurate to 6 decimal places.)
P(1)=\displaystyle {P}{\left({1}\right)}=

Find the relative difference between the two values.
Recall, the formula
approximationactualactual100%\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 = %