Use the Frequency Distribution to Find the Mean and the Sample

question 105

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.

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