Chicago Commute Times: The following are $15$ commute times in minutes for a random sample of Chicago residents: $10,35,20,15,60,10,30,45,10,55,20,10,25,40,10$. Construct a $99\%$ confidence interval for the population mean commute time. Is this interval a precise estimate of the mean?

$(22.15\text{ min},30.51\text{ min})$, it is not precise because the sample size is very large

$(22.15\text{ min},30.51\text{ min})$, it is precise because the mean falls within the interval

$(13.14\text{ min},39.52\text{ min})$, it is not precise because the interval is too wide

$(13.14\text{ min},39.52\text{ min})$, it is precise because the mean falls within the interval