Question

find the area under the standard normal curve to the right of ( z = 1 ).

Explanation:

Step1: Recall the properties of the standard normal distribution

The total area under the standard normal curve is \(1\). The area to the left of \(z = 1\) can be found using the standard normal table (z - table).

Step2: Look up the value in the z - table

From the standard normal table, the area to the left of \(z=1\) is \(P(Z < 1)=0.8413\).

Step3: Calculate the area to the right of \(z = 1\)

The area to the right of \(z = 1\) is \(P(Z>1)=1 - P(Z < 1)\). Substitute \(P(Z < 1)=0.8413\) into the formula: \(P(Z>1)=1 - 0.8413=0.1587\)

Answer:

A. \(0.1587\)