The diameter of a mason jar is $3$ inches but can be as large as $3\mathrm{.}03$ inches and as small as $2\mathrm{.}97$ inches. Twenty$-$five samples of mason jars are taken and it is discovered that these components have a grand mean of $3\mathrm{.}01$ inches and a standard deviation of $0\mathrm{.}02$ inches. What is the probability of producing a bad product?

Group of answer choices

$0\mathrm{.}18$

$0\mathrm{.}45$

$0\mathrm{.}33$

$0\mathrm{.}84$

$0\mathrm{.}60$