Question

find the indicated area under the standard normal curve. between z = - 0.83 and z = 0.83 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 = - 0.83 and z = 0.83 under the standard normal curve is . (round to four decimal places as needed.)

Explanation:

Step1: Use standard - normal table property

The standard - normal distribution is symmetric about \(z = 0\). The area to the left of \(z = 0.83\) is \(P(Z<0.83)\), and the area to the left of \(z=- 0.83\) is \(P(Z < - 0.83)\).
From the standard - normal table, \(P(Z<0.83)=0.7967\) and \(P(Z < - 0.83)=1 - P(Z<0.83)=1 - 0.7967 = 0.2033\).

Step2: Calculate the area between \(z=-0.83\) and \(z = 0.83\)

The area between \(z=-0.83\) and \(z = 0.83\) is \(P(-0.83<Z<0.83)=P(Z<0.83)-P(Z < - 0.83)\).
Substitute the values: \(P(-0.83<Z<0.83)=0.7967-0.2033 = 0.5934\).

Answer:

\(0.5934\)