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Let z1 be the smaller z value and z2 be the larger value. Let N(z) be the cumulative normal distribution evaluated at some value z. The random variable is Z.
The probability that Z has a value from minus infinity to z2 is equal to N(z2). You can show this by drawing a bell shape curve, and shading in everything to the left of z2 as equal to the area under curve.
Similarly, the probability that Z has a value from minus infinity to z1 is N(z1).
The area under the bell curve (standard normal cumulative distribution) is N(z1) - N(z2). I can show this with a little example:
z1= -1 z2 = 2 Area = N(2) - N(-1) = 0.9773 - 0.1587 = 0.8186. I used Excel with the normsdist(z) function. The mean is zero and standard deviation is one with this function.
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What is the area under the normal curve between Z0.0 and Z1.79?
What is the area under the normal curve between z=0.0 and z=1.79?
What is the area under the standard normal curve?
the standard normal curve 2
How is probability related to the area under the normal curve?
The Normal curve is a graph of the probability density function of the standard normal distribution and, as is the case with any continuous random variable (RV), the probability that the RV takes a value in a given range is given by the integral of the function between the two limits. In other words, it is the area under the curve between those two values.
What is the area under the normal curve between z equals 0.0 and z equals 2.0?
What is the area under the normal curve between z equals 0.0 and z equals 2.0?
What is the area between z equals 0 and z equals 2.24?
The question does not specify what z is but this answer will assume that it is the value of a random variable with a Standard Normal distribution. That being the case, the area under the curve between those values is 0.4875.
