Find an interval. Needing help! HELP

Question

1. A dataset with mean 78 and standard deviation 5 has a symmetric bell-shaped distribution. Find an interval that is likely to contain about 95 % of the data values.

2. Use the 95 % 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 95 % of the data values.

A bell-shaped distribution with mean 1100 and standard deviation 15

Answer 1

Hi Brittany,

 

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)

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.