The pulse rates of $157$ randomly selected adult males vary from a low of $38bpm$ to a high of $106bpm.$ Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want $98\%$ confidence that the sample mean is within $4$ bpm of the population mean. Complete parts $($a$)$ through $($c$)$ below.

a$.$ Find the sample size using the range rule of thumb to estimate $.$

$n=$

$($Round up to the nearest whole number as needed.$)$