Use the frequency distribution to find the mean and the sample standard deviation. Does the data form a normal distribution? Remember: if the data fall within 2% of the empirical rule of 68%, 95%, and 99.7% for one, two, or three standard deviations, respectively, they form a normal distribution. $\begin{array} { | l | l | }
\hline \text { Shipment time (hours) } & \text { Frequency } f \
\hline 23.5 - 28.5 & 19 \
\hline 28.5 - 33.5 & 417 \
\hline 33.5 - 38.5 & 789 \
\hline 38.5 - 43.5 & 698 \
\hline 43.5 - 48.5 & 504 \
\hline 48.5 - 53.5 & 42 \
\hline
\end{array}$
A) The mean is 45 hours. The sample standard deviation is 5 hours. The data doesn't form a normal distribution.
B) The mean is 39 hours. The sample standard deviation is 5 hours. The data doesn't form a normal distribution.
C) The mean is 39 hours. The sample standard deviation is 5 hours. The data forms a normal distribution.
D) The mean is 35 hours. The sample standard deviation is 5 hours. The data doesn't form a normal distribution.
E) The mean is 45 hours. The sample standard deviation is 5 hours. The data forms a normal distribution.

Question

Use the frequency distribution to find the mean and the sample standard deviation. Does the data form a normal distribution? Remember: if the data fall within 2% of the empirical rule of 68%, 95%, and 99.7% for one, two, or three standard deviations, respectively, they form a normal distribution.   $\begin{array} { | l | l | } 
\hline \text { Shipment time (hours) } & \text { Frequency } f \
\hline 23.5 - 28.5 & 19 \
\hline 28.5 - 33.5 & 417 \
\hline 33.5 - 38.5 & 789 \
\hline 38.5 - 43.5 & 698 \
\hline 43.5 - 48.5 & 504 \
\hline 48.5 - 53.5 & 42 \
\hline
\end{array}$
A) The mean is 45 hours. The sample standard deviation is 5 hours. The data doesn't form a normal distribution.
B) The mean is 39 hours. The sample standard deviation is 5 hours. The data doesn't form a normal distribution.
C) The mean is 39 hours. The sample standard deviation is 5 hours. The data forms a normal distribution.
D) The mean is 35 hours. The sample standard deviation is 5 hours. The data doesn't form a normal distribution.
E) The mean is 45 hours. The sample standard deviation is 5 hours. The data forms a normal distribution.

Quizplus · Accepted Answer

To calculate the mean and standard deviation, we first find the midpoint of each class by averaging the lower and upper bounds. Then, multiply each midpoint by the class frequency to find the "weighted" midpoints, sum these products, and divide by the total number of observations to get the mean. The calculation of standard deviation involves using the squared differences between each class midpoint and the mean, weighted by the class frequencies. Without performing the exact calculations here, the correct choice is based on understanding the distribution's shape and properties. Given the distribution's skew, it's unlikely to perfectly follow a normal distribution, especially if the empirical rule doesn't closely match.

Use the Frequency Distribution to Find the Mean and the Sample