Find the area under the standard normal distribution curve between z = 0 and z = 2.16.

Solution:

The normal distribution is defined by the probability density function f(x) for the continuous random variable X considered in the system.

It is a function whose integral across an interval (say x to x + dx) gives the probability of the random variable X, by considering the values between x and x + dx. 

A Z-Score chart, often called a Z-Table, is used to find the area under a normal curve, or bell curve, for a binomial distribution.

The Z score itself is a statistical measurement of the number of standard deviations from the mean of a normal distribution.

Using the z-chart table

When z = 0,

we see that z = 0.50000

When z = 2.16,

we see that z = 0.9846

By subtracting both we can find the area under the standard normal distribution curve

Area = 0.9846 - 0.50000

= 0.4846

Therefore, the area under the standard normal distribution curve is 0.4846.

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Find the area under the standard normal distribution curve between z = 0 and z = 2.16.

Summary:

The area under the standard normal distribution curve between z = 0 and z = 2.16 is 0.4846.