Use the rule and the fact that the summary statistics come from a distribution that is symmetric and bell-shaped to find an interval that is expected to contain about
of the data values.

A bell-shaped distribution with mean 230 and standard deviation 29 .

In Statistics, if the set of data values are normally distributed in a bell shaped curve, the following data point percentages exist:

   1.  68% of the data points will lie within one STD of the Mean.

   2.  95% of the data points will lie within two STDs of the Mean.

   3.  99% of the data points will lie within three STDs of the Mean.

Applying the above rules, we can answer our two questions:

   1.  Set of Data (Mean = 78; STD = 5)

            78 - 2(5) = 78 - 10 = 68

            78 + 2(5) = 78 + 10 = 88

            95% Rule:  68 - 88 (range of data points)

   2.  Set of Data (Mean = 1100; STD = 15)

            1100 - 2(5) = 1100 - 10 = 1090

            1100 + 2(5) = 1100 + 10 = 1110

            95% Rule:  1090 - 1110

                             (range of data points)

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step-by-step explanation: