A normal distribution is defined as a distribution whose mode, mean and median are equal and occurs naturally in numerous situation. The spread of distribution is usually controlled by the standard deviation. The measures of dispersion from average are represented by intervals µ - σ to µ + σ, µ - 2σ to µ + 2σ and µ - 3σ to µ + 3σ. In other words, it means that about 68%, 95% and 99.7% of data are within one standard deviation, two standard deviations and three standard deviations respectively. As a result, a bell-shaped curve is created.
For purposes of this posting, I will consider my own scenario of cycling from home to the nearby shopping mall. On average, to reach the shopping mall, I take 20 minutes. However, this is sometimes accustomed to a standard deviation of 3 minutes. i.e., sometimes I would be early and sometimes late.
Delegate your assignment to our experts and they will do the rest.
Therefore, applying the 68-95-99.7% rule, I can be able to calculate the dispersion. i.e.,
For 68% (µ - σ to µ + σ)
= 20-3 to 20.3
= 17 to 23 therefore 68% of my cycling time lie between 17 and 23 minutes.
For 95% (µ - 2σ to µ + 2σ)
= 14 to 26 minutes hence 95% of my cycling time is within the interval of 14 and 26 minutes
For 99.7% (µ - 3σ to µ + 3σ)
The cycling times lies within the interval of 11 and 29 minutes.
These time intervals are distributed as shown below
68%
95%
99.7%
