How To Find Area Under A Normal Curve?

A normal distribution is a symmetrical distribution. In a normal distribution mean, mode and median of the data set are equal. All values are cluster around the mean or average in a normal distribution. The normal curve is a bell shaped and the total area under the curve is equal to one. Normal distribution is based on two parameters that are mean and variance.

Z= [x- mean]/ standard deviation

For each value of x we get different values of z. These values are checked in area table to find the value of area under the curve.
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Find the percent of the total area under the curve between z = -2.36 and z = -0.14
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Normal distibution is a continuous distribution and every distribution follows normal distribution when sample size is large. It has two parameters, one is mean and second one is standard deviation.
When mean = 0 and Sd = 1, normal distribution change into standard normal distribution and curve is known as standard normal curve.
Z = (x- mean)/standard deviation

For each value of x we get different values of z. The area under curve of value of z  is calculate from using normal area curve table.

Total area under the curve between z= -2.36 and z= -0.14
= Area under curve between z= -2.36 and z= 0 - Area uder curve between                    z = -0.14  and z= 0
= Prob (Z=-2.36 and Z=0) - Prob (Z= -.14 and Z=0)
= 0.4904 - 0..0557
= 0.4347
Percent of the total area under the curve between z = -2.36 and z = -0.14
= 0.4347 *100
= 43.47%
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