**Properties of normal curve.**

Normal curve has bell shaped and the curve is symmetric about it’s mean. The curve is completely determined by the **mean (μ)** and the **standard deviation (σ)**. The area under the curve to the right of the mean is 0.5 and the area under the curve to the left of the mean is 0.5.

According to empirical rule

• approximately 68% of the measurements will fall within 1 standard deviations of the mean, i.e. within the interval ( μ− 1*σ, μ + 1*σ)

• approximately 95% of the measurements will fall within 2 standard deviations of the mean, i.e. within the interval ( μ− 2*σ, μ + 2*σ)

• approximately 99.7% of the measurements will fall within 3 standard deviations of the mean, i.e. within the interval ( μ− 3*σ, μ + 3*σ)

Using all those properties the normal curve for X variable with mean( μ ) 100 and standard deviation (σ) 10 is