Question

find the area under the standard normal distribution curve between ( z = 0 ) and ( z = 0 ). use the standard normal distribution table. round your answer to at least 4 decimal places.
the area between the two ( z ) values is

Explanation:

Step1: Recall the property of the standard normal distribution

The standard normal distribution is symmetric about \(z = 0\). The area under the standard normal curve from \(z=a\) to \(z = b\) when \(a=b\) is calculated as follows.

Step2: Use the formula for the area between two \(z\) - values

The formula for the area between \(z_1\) and \(z_2\) is \(A=\Phi(z_2)-\Phi(z_1)\), where \(\Phi(z)\) is the cumulative distribution function of the standard normal distribution. When \(z_1 = 0\) and \(z_2=0\), we have \(A=\Phi(0)-\Phi(0)\)

Since \(\Phi(0)=0.5\) (from the standard normal distribution table, the cumulative probability for \(z = 0\) is \(0.5\)), then \(A=0.5 - 0.5\)

Answer:

\(0.0000\)