Standard Normal Curve Calculator

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Standard normal curve is a bell shaped curve that represents the normal distribution of probability over the values of random variable, also called probability density function. The mean of the standard normal curve is zero and standard deviation is 1. The mean tells the center and the standard deviation tells the height and width of the bell. Normal curve helps to find the probability of a n observation to fall into an interval within the normal curve. This interval is the area of that interval under the normal curve. This normal distribution is also referred as Gaussian distribution. The standard normal  curve calculator is used to  find the area under the normal distribution when z score is provided.

A normal curve can to converted to standard normal curve by the formula

Z = X – mean/ Std deviation

Percentages of the area of the curve with standard deviation 1, 2 and 3 is given by

-1<= Z <= 1  68.27%

-2<= Z <= 2  95.45%

-3 >= Z <= 3 99.73%

Any positive value of z is found in z-table.

Example 1:  Find the area under the right of 1.06 under the standard normal curve.

In this case we consider the full right hand side area = 0.5. Then subtract the area between 0 and 1.06 using the z table.

P(Z>1.06) = 0.5 – P(0
0.5 – 0.355 = 0.1446

Example 2:  Find the area between 1.06 and 4.00 under the standard normal curve.

We will do the following

P(0 < Z < 4.00) = P(0< Z < 1.06)

= 0.5 – 0.3554

= 0.1446.


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