Question

use this table or the aleks calculator to complete the following. give your answers to four decimal places (for example, 0.1234). (a) find the area under the standard normal curve to the right of z = 0.85. (b) find the area under the standard normal curve between z = 0.82 and z = 2.20.

Explanation:

Step1: Recall the property of the standard - normal distribution

The total area under the standard - normal curve is 1, and the cumulative - distribution function of the standard - normal distribution $\varPhi(z)$ gives the area to the left of $z$.

Step2: Calculate the area to the right of $z = 0.85$

The area to the right of $z$ is $1-\varPhi(z)$. Looking up $\varPhi(0.85)$ in the standard - normal table or using a calculator, $\varPhi(0.85)=0.8023$. So the area to the right of $z = 0.85$ is $1 - 0.8023=0.1977$.

Step3: Calculate the area between $z = 0.82$ and $z = 2.20$

The area between $z_1$ and $z_2$ is $\varPhi(z_2)-\varPhi(z_1)$. Looking up $\varPhi(0.82)$ and $\varPhi(2.20)$ in the standard - normal table or using a calculator, $\varPhi(0.82)=0.7939$ and $\varPhi(2.20)=0.9861$. Then $\varPhi(2.20)-\varPhi(0.82)=0.9861 - 0.7939 = 0.1922$.

Answer:

(a) 0.1977
(b) 0.1922