Question

find the area under the standard normal distribution curve to the right of ( z = 2.58 ). use the standard normal distribution table and enter the answer to 4 decimal places. the area to the right of the ( z ) value is

Explanation:

Step1: Find the cumulative area for \(z = 2.58\)

Using the standard - normal distribution table (z - table), for \(z=2.58\), the cumulative area \(P(Z\leq2.58)\) is found. Looking up \(z = 2.5\) in the left - most column and \(0.08\) in the top row. The value in the table is \(0.9951\).

Step2: Calculate the area to the right of \(z = 2.58\)

The total area under the standard - normal curve is \(1\). The area to the right of \(z\) is given by \(P(Z > z)=1 - P(Z\leq z)\).
Substitute \(z = 2.58\) and \(P(Z\leq2.58)=0.9951\) into the formula: \(P(Z>2.58)=1 - 0.9951\)

Answer:

\(0.0049\)