Use the Frequency Distribution to Find the Mean and the Sample

Multiple Choice

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.   $\begin{array}{|ccc|}\hline \text {Weight (lb) } & \text { Midpoint x }& \text {Frequency t }\\\hline 1.5-10.5 && 12 \\10.5-19.5 && 39 \\19.5-28.5 && 120 \\28.5-37.5 && 207 \\37.5-46.5 && 368 \\46.5-55.5 && 344 \\55.5-64.5 && 222 \\64.5-13.5 && 100 \\13.5-82.5 && 30 \\82.5-91.5 && 12\\\hline\end{array}$

A) The mean is 36 lb. The sample standard deviation is 10.4 lb. The data forms a normal distribution.
B) The mean is 36 lb. The sample standard deviation is 10.4 lb. The data doesn't form a normal distribution.
C) The mean is 46 lb. The sample standard deviation is 14.6 lb. The data doesn't form a normal distribution.
D) The mean is 38 lb. The sample standard deviation is 13.6 lb. The data doesn't form a normal distribution.
E) The mean is 46 lb. The sample standard deviation is 14.6 lb. The data forms a normal distribution.