The annual earnings$($in dollars$)$ of $35$ randomly selected microbiologists are shown in the data table. Use the data to$($a$)$ find the sample$$ mean, $($b$)$ find the sample standard$$ deviation, and$($c$)$ construct a$98\%$ confidence interval for the population mean.

$100,653$

$81,086$

$78,548$

$67,372$

$51,200$

$67,594$

$93,887$

$65,602$

$79,691$

$74,414$

$44,619$

$86,298$

$60,571$

$58,035$

$55,140$

$78,213$

$47,553$

$99,516$

$81,285$

$92,548$

$63,664$

$74,364$

$50,782$

$61,014$

$92,006$

$84,266$

$79,744$

$63,974$

$74,537$

$57,245$

$46,665$

$89,020$

$75,481$

$61,643$

$82,133$

Question content area bottom

Part $1$

$($a$)$ Find the sample mean.

x$=$enter your response here $($Type an integer or decimal rounded to two decimal places as$$ needed.$)$