A random sample of hotdogs of a particular brand has an average fat content of $3$ grams. How large a sample should be taken so that the sample average is within $0\mathrm{.}27$ gram of the true average with confidence coefficient $48\%($Assume that the fat content ranges from $1\mathrm{.}62$ grams to $4\mathrm{.}26$ grams$).$

a$)3$

b$)2$

c$)7$

d$)4$