Use the empirical rule for normal distribution to find what two values 95% of the data will fall between for a data set with a mean of 272 and standard deviation of 14.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

For data that can be arranged in a normal distribution 95% of the data values fall within `+-2 sigma` of the mean (`mu` ) where sigma is the standard deviation.

Here, sigma is equal to 14 and the mean is 272.

95% of the data falls within the values 272 + 14*2 = 300 and 272 - 14*2 = 244

Using the empirical rule, 95% of values fall between 244 and 300

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sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You should know that for a normal distribution, 95% of the data fall within 2 standard deviations, hence, you need to multiply the standard deviation `sigma=14`  by 2, such that:

`14*2 = 28`

Now, you need to subtract and add 28 to the given mean `mu = 272 ` to find the end data of interval such that:

`mu+-sigma = 272+-28 => {(mu+sigma = 300),(mu-sigma=244):}`

Hence, evaluating the two values under the given conditions yields `mu+sigma = 300`  and `mu-sigma=244` .

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