Given a normal distribution with μ = 69 and σ = 2.8, calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges

## Calculate Range 1:

Range 1, or the 68% range, states that 68% of the normal distribution values lie within 1 standard deviation of the mean

68% of values are within μ ± σ

μ ± σ = 69 ± 2.8

69 - 2.8 <= 68% of values <= 69 + 2.8

**66.2 <= 68% of values <= 71.8**## Calculate Range 2:

Range 2, or the 95% range, states that 95% of the normal distribution values lie within 2 standard deviations of the mean

95% of values are within μ ± 2σ

μ ± 2σ = 69 ± 2(2.8)

69 - 2 x 2.8 <= 95% of values <= 69 + 2 x 2.8

69 - 5.6 <= 95% of values <= 69 + 5.6

**63.4 <= 95% of values <= 74.6**## Calculate Range 3:

Range 3, or the 99.7% range, states that 99.7% (virtually ALL) of the normal distribution values lie within 3 standard deviations of the mean

99.7% of values are within μ ± 3σ

μ ± 3σ = 69 ± 3(2.8)

69 - 3 x 2.8 <= 99.7% of values <= 69 + 3 x 2.8

69 - 8.4 <= 99.7% of values <= 69 + 8.4

**60.6 <= 99.7% of values <= 77.4**

##### What is the Answer?

**60.6 <= 99.7% of values <= 77.4**

##### How does the Normal Distribution Calculator work?

Free Normal Distribution Calculator - Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).

Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability

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### What 1 formula is used for the Normal Distribution Calculator?

### What 9 concepts are covered in the Normal Distribution Calculator?

- distribution
- value range for a variable
- empirical rule
- Provides estimate for the spread of data in a normal distribution. 68% of the data will fall within one standard deviation of the mean. 95% of the data will fall within two standard deviations of the mean. 99.7% of the data will fall within three standard deviations of the mean
- event
- a set of outcomes of an experiment to which a probability is assigned.
- mean
- A statistical measurement also known as the average
- normal distribution
- an arrangement of a data set in which most values cluster in the middle of the range and the rest taper off symmetrically toward either extreme.
- probability
- the likelihood of an event happening. This value is always between 0 and 1.

P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes - standard deviation
- a measure of the amount of variation or dispersion of a set of values. The square root of variance
- variance
- How far a set of random numbers are spead out from the mean
- z score
- the number of standard deviations from the mean a data point is. Also known as a standard score

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