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A normal distribution has a mean of 36 and a standard deviation of 5. Find the range of values that represent the middle68% of the distribution.

User Festus
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1 Answer

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Given:

The mean of the normal distribution is 36.


\mu=36

The standard deviation is 5.


\sigma=5

The distribution percent is 68 %.

Required:

We need to find the range of the values that represent the middle 68% of the distribution.

Step-by-step explanation:

Recall that 68% of the data is within 1 standard deviation (σ) of the mean (μ),

Consider the range formula for within 1 standard deviation (σ) of the mean (μ),


Range=(\mu-\sigma,\mu+\sigma)
Substitute\text{ }\mu=36,\text{ and }\sigma=5\text{ in the formula.}


Range=(36-5,36+5)
Range=(31,41)

Final answer:


Range=(31,41)

User Jegtugado
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