The book Code Complete by Steve McDonnell estimates that there are $15$ to $50$ errors per $1000$ lines of delivered code for computer programs. Assume that for a particular software package, the error rate is $28$ per $1000$ lines of code and that the number of errors per $1000$ lines of code follows a Poisson distribution.

a$.$ What is the probability that a portion of code for this computer package that contains $250$ lines of code contains no errors? $($to $4$ decimals$)$

$0\mathrm{.}0009$

b$.$ What is the probability of there being exactly $25$ errors in $1000$ lines of code? $($to $4$ decimals$)$

c$.$ What is the probability of more than three errors in $100$ lines of code? $($to $4$ decimals$)$

d$.$ What is the expected number of errors in a portion of code that contains $22000$ lines of code? $($to $0$ decimal$)$

$616$