The book Code Complete by Steve McDonnell estimates that there are $15$ to $50$ errors per $1,000$ lines of delivered code for computer programs. Assume that for a particular software package, the error rate is $17$ per $1,000$ lines of code and that the number of errors per $1,000$ 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? $($Round your answer to four decimal places.$)$

Enter a number.

$($b$)$ What is the probability of there being exactly $22$ errors in $1,000$ lines of code? $($Round your answer to four decimal places.$)$

$($c$)$ What is the probability of more than three errors in $100$ lines of code? $($Round your answer to four decimal places.$)$

$($d$)$ What is the expected number of errors in a portion of code that contains $25,000$ lines of code?