Question

Every normally distributed variable has specific features and characteristics that enable a person to draw the curve just from knowing the mean and standard deviation. What are those features? Name and describe four features of a normal curve, including what the "68-95-99.7 Rule" can tell you about the dispersion of the data

Answer 1

the four features of a normal curve are:-

1. all normal distribution curve are symmetric about the mean ().the height of any normal curve is maximum at . for normal distribution, mean =median=mode.

2. normal curves are symmetric.All normal curves are bell-shaped. The shape of normal curve depends on its mean  and standard deviation σ.

3.The total area under the curve is equal to 1 .

4.to approximate the area that falls within a specific sd from the mean we use the empirical rule, that is:-

approximately 68 % of data lies within ()

approximately 95 % of data lies within ()

approximately 99.7 % of data lies within ()

where, is the standard deviation.

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