Find the requested confidence interval.
-A college statistics professor has office hours from 9:00 A.M. to $10 : 30$ A.M. daily. A sample of waiting times to see the professor (in minutes) is $10,12,20,15,17,10,30,28,35,28,19,27,25,22,33$, $37,14,21,20,23$. Assuming $\sigma = 7.84$, find the $99.74 \%$ confidence interval for the population mean.
A)$18.8$ to $25.8$ minutes
B) $19.5$ to $35.1$ minutes
C) $17.05$ to $27.55$ minutes
D) $20.55$ to $24.05$ minutes

Question

Find the requested confidence interval.
-A college statistics professor has office hours from 9:00 A.M. to $10 : 30$ A.M. daily. A sample of waiting times to see the professor (in minutes) is $10,12,20,15,17,10,30,28,35,28,19,27,25,22,33$, $37,14,21,20,23$. Assuming $\sigma = 7.84$, find the $99.74 \%$ confidence interval for the population mean.  
A)$18.8$ to $25.8$ minutes
B) $19.5$ to $35.1$ minutes
C) $17.05$ to $27.55$ minutes
D) $20.55$ to $24.05$ minutes

Quizplus · Accepted Answer

Given a sample size $n = 20$, sample mean $\bar{x}$ can be calculated as the sum of all sample values divided by 20. The population standard deviation is given as $\sigma = 7.84$. For a $99.74\%$ confidence interval, the Z-score associated is approximately $3$ (since $99.74\%$ corresponds to $3$ standard deviations on either side of the mean in a normal distribution). The confidence interval formula is $\bar{x} \pm Z \frac{\sigma}{\sqrt{n}}$. Calculating the sample mean $\bar{x} = \frac{10+12+20+15+17+10+30+28+35+28+19+27+25+22+33+37+14+21+20+23}{20} = 22.3$. The margin of error $E = 3 \times \frac{7.84}{\sqrt{20}} \approx 5.25$. Thus, the confidence interval is $22.3 \pm 5.25$, which is approximately $17.05$ to $27.55$.

Find the Requested Confidence Interval 10:3010 : 3010:30 AM Daily a Sample of Waiting Times to See the Professor

Find the Requested Confidence Interval $10 : 30$ AM Daily a Sample of Waiting Times to See the Professor