Part $1(6$ points$)$

For each random variable, state whether the random variable should be modeled with a Binomial distribution or a Poisson distribution. Explain your reasoning. State the parameter values that describe the distribution and give the probability mass function.

Random Variable $1(3$ points$)$

A software development team is concerned with the performance of their code. Historically, $3\%$ of code modules exhibit performance issues. A development team samples $25$ code modules from a project. Assuming the chance of performance issues is independent between modules, what type of distribution could be used to model the number of successful code modules from the sample of $25?$ Hint: the event of interest here is a code module performing well $($i$.$e$.,$ not exhibiting performance issues$).$