Find the area under the standard normal curve between z = 0 and z = 3.
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 = 0.5000
When z = 3,
we see that z = 0.9987
By subtracting both we can find the area under the standard normal distribution curve
Area = 0.9987 - 0.5000
= 0.4987
Therefore, the area under the curve is 0.4987
Find the area under the standard normal curve between z = 0 and z = 3.
Summary:
The area under the normal curve between z = 0 and z = 3 is 0.4987