Question

find the indicated area under the standard normal curve. between z = - 2.46 and z = 2.46 click here to view page 1 of the standard normal table. click here to view page 2 of the standard normal table. the area between z = - 2.46 and z = 2.46 under the standard normal curve is (round to four decimal places as needed.)

Explanation:

Step1: Recall standard - normal table property

The standard - normal distribution is symmetric about \(z = 0\). The total area under the standard - normal curve is 1. The area to the left of \(z = 0\) is 0.5 and the area to the right of \(z = 0\) is 0.5.

Step2: Find the area to the left of \(z=-2.46\)

Looking up \(z=-2.46\) in the standard - normal table, the area to the left of \(z =-2.46\) is \(A_1=\Phi(-2.46)\). From the standard - normal table, \(\Phi(-2.46)=0.0069\).

Step3: Find the area to the left of \(z = 2.46\)

Looking up \(z = 2.46\) in the standard - normal table, the area to the left of \(z = 2.46\) is \(A_2=\Phi(2.46)\). Since the standard - normal distribution is symmetric, \(\Phi(2.46)=1 - \Phi(-2.46)\). So \(\Phi(2.46)=1 - 0.0069=0.9931\).

Step4: Calculate the area between \(z=-2.46\) and \(z = 2.46\)

The area between \(z=-2.46\) and \(z = 2.46\) is \(A=A_2 - A_1\). Substituting the values of \(A_1\) and \(A_2\), we get \(A = 0.9931-0.0069 = 0.9862\).

Answer:

\(0.9862\)